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Publications of the Research Institute for Mathematical Sciences
Publ. Res. Inst. Math. Sci.
PRIMS
0034-5318
1663-4926
General
10.4171/PRIMS
http://www.ems-ph.org/doi/10.4171/PRIMS
subscribers, moving wall 5 years
European Mathematical Society Publishing House
Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
44
2008
1
A Presentation of Lie Tori of Type Bℓ
Malihe
Yousofzadeh
University of Isfahan, ISFAHAN, IRAN
We give a finite presentation of the universal covering algebra of a Lie torus of type Bℓ, ℓ ≥ 3.
Nonassociative rings and algebras
General
1
44
10.2977/prims/1207921074
http://www.ems-ph.org/doi/10.2977/prims/1207921074
Corrigendum to “Decay of Solutions of Wave-type Pseudo-differential Equations over p-adic Fields”
W.
Zúñiga-Galindo
CINVESTAV–I.P.N., SANTIAGO DE QUERÉTARO, QRO., MEXICO
Non-archimedan pseudo-differential equations, restriction of Fourier transforms, exponential sums modulo pm, Igusa local zeta function
Partial differential equations
Number theory
Operator theory
General
45
48
10.2977/prims/1207921075
http://www.ems-ph.org/doi/10.2977/prims/1207921075
Notes on Microstate Free Entropy of Projections
Fumio
Hiai
, ABIKO, JAPAN
Yoshimichi
Ueda
Kyushu University, HAKOZAKI, FUKUOKA, JAPAN
We study the microstate free entropy χproj(p1 , . . . , pn) of projections, and establish its basic properties similar to the self-adjoint variable case. Our main contribution is to characterize the pair-block freeness of projections by the additivity of χproj (Theorem 4.1), in the proof of which a transportation cost inequality plays an important role. We also briefly discuss the free pressure in relation to χproj.
Functional analysis
Linear and multilinear algebra; matrix theory
Probability theory and stochastic processes
Information and communication, circuits
49
89
10.2977/prims/1207921076
http://www.ems-ph.org/doi/10.2977/prims/1207921076
Simultaneous Linearization of Holomorphic Maps with Hyperbolic and Parabolic Fixed Points
Tetsuo
Ueda
Kyoto University, KYOTO, JAPAN
We study local holomorphic mappings of one complex variable with parabolic fixed points as a limit of a families of mappings with attracting fixed points. We show that the Fatou coordinate for a parabolic fixed point can be obtained as a limit of some linear function of the solutions to Schröder equation for perturbed mappings o with attracting fixed points.
Functions of a complex variable
Dynamical systems and ergodic theory
General
91
105
10.2977/prims/1207921077
http://www.ems-ph.org/doi/10.2977/prims/1207921077
Asymptotics of the Spectral Density for Radial Dirac Operators with Divergent Potentials
Michael
Eastham
University of Wales Cardiff, CARDIFF, UNITED KINGDOM
Karl Michael
Schmidt
University of Wales Cardiff, CARDIFF, UNITED KINGDOM
We study the asymptotics of the spectral density of one-dimensional Dirac systems on the half-line with an angular momentum term and a potential tending to infinity at infinity. The problem has two singular end-points; however, as the spectrum is simple, the derivative of the spectral matrix has only one non-zero eigenvalue which we take to be the spectral density. Our main result shows that, assuming sufficient regularity of the potential, there are no points of spectral concentration for large values of the spectral parameter outside a neighbourhood of a discrete set of exceptional points.
Ordinary differential equations
Operator theory
Quantum theory
General
107
129
10.2977/prims/1207921078
http://www.ems-ph.org/doi/10.2977/prims/1207921078
On the Presentations of Extended Affine Weyl Groups
Saeid
Azam
University of Isfahan, ISFAHAN, IRAN
Valiollah
Shahsanaei
University of Isfahan, ISFAHAN, IRAN
We give a finite presentation for reduced non-simply laced extended affine Weyl groups of arbitrary nullity. When nullity is less than or equal to 3, this presentation reduces to a very simple presentation in which the generators and relations can be easily read from a set of data attached to the root system.
Group theory and generalizations
Nonassociative rings and algebras
General
131
161
10.2977/prims/1207921079
http://www.ems-ph.org/doi/10.2977/prims/1207921079
Retraction Notice
Retraction of “Infinite Dimensionality of the Middle L2 -cohomology on Non-compact Kähler Hyperbolic Manifolds” [Publications of the Research Institute for Mathematical Sciences, 42 (2006), 683–689, Bo Yong Chen, Department of Mathematics, Tongji University, Shanghai 200092, P.R. China] This article has been retracted at the request of the editor-in-chief and the author. Reason: There is a gap in the proof of Theorem 1, which has been pointed out by Dr. Kazuhisa Miyazawa. The editorial board apologizes for any inconveniences this may cause.
Manifolds and cell complexes
General
163
163
10.2977/prims/1207921080
http://www.ems-ph.org/doi/10.2977/prims/1207921080
2
Preface
The present issue of Publications of RIMS is dedicated to Professor Heisuke Hironaka on the occasion of his Kiju∗ , that is, his 77th birthday. Professor Hironaka was born on April 9, 1931 in Yamaguchi Prefecture. After receiving his Bachelor of Science in 1954 and his Master of Science in 1956 both from Kyoto University, he received his Ph. D. from Harvard University in 1960. After years at Brandeis, Colombia and Harvard Universities, he became a professor of RIMS Kyoto University in 1975. He was Director of RIMS from 1983 to 1985, and has been a Professor Emeritus of Kyoto University since 1991. Professor Hironaka began his study of algebraic geometry in the graduate school of Kyoto University. He solved “the resolution of singularities”, one of the most fundamental problems in mathematics in 1960’s, and constructed and developed deep theories in algebraic geometry (see the article by Lê Dũng Tráng and Bernard Teissier in the present issue). He was awarded the Japan a Academy Prize and the Fields Medal both in 1970. Among many other honors he received an Order of Cultural Merits from Japanese Government in 1975. Professor Hironaka has also made great efforts to bring up young mathematical scientists and to develop international exchange in mathematical sciences (see the article by Tadao Oda in the present issue). This issue consists of 16 invited articles, all of which are fully refereed. We are grateful to the authors. We would like to express our deepest gratitude to Professor Hironaka for his great academic and educational achievements on this occasion. Masaki Kashiwara Shigefumi Mori Shigeru Mukai Kyoji Saito Yum-Tong Siu Bernard Teissier Stephen S.-T. Yau ∗ 喜寿: joyful and long life. The first letter in sousyo, a running style, is very similar to the Chinese numeral, 77.
General
0
0
10.2977/prims/1210167323
http://www.ems-ph.org/doi/10.2977/prims/1210167323
On the Mathematical Work of Professor Heisuke Hironaka
Lê Dũng
Tráng
ICTP, TRIESTE, ITALY
Bernard
Teissier
UMR 7586 du CNRS, PARIS CEDEX 13, FRANCE
Algebraic geometry
General
165
177
10.2977/prims/1210167324
http://www.ems-ph.org/doi/10.2977/prims/1210167324
Professor Heisuke Hironaka’s Contribution in Promoting Mathematical Sciences and Bringing up Talent in New Generations
Tadao
Oda
University of Tokyo, TOKYO, JAPAN
Algebraic geometry
General
179
182
10.2977/prims/1210167325
http://www.ems-ph.org/doi/10.2977/prims/1210167325
Holonomy Groups of Stable Vector Bundles
V.
Balaji
Chennai Mathematical Institute, SIRUSERI, INDIA
János
Kollár
Fine Hall / Princeton University, PRINCETON, UNITED STATES
We define the notion of holonomy group for a stable vector bundle F on a variety in terms of the Narasimhan–Seshadri unitary representation of its restriction to curves. Next we relate the holonomy group to the minimal structure group and to the decomposition of tensor powers of F. Finally we illustrate the principle that either the holonomy is large or there is a clear geometric reason why it should be small.
Algebraic geometry
Several complex variables and analytic spaces
Differential geometry
General
183
211
10.2977/prims/1210167326
http://www.ems-ph.org/doi/10.2977/prims/1210167326
A φ1,3-Filtration of the Virasoro Minimal Series M(p, p') with 1 < p'/p < 2
E.
Feigin
Independent University of Moscow, MOSCOW, RUSSIAN FEDERATION
Boris
Feigin
Independent University of Moscow, MOSCOW, RUSSIAN FEDERATION
M.
Jimbo
University of Tokyo, TOKYO, JAPAN
Tetsuji
Miwa
Kyoto University, KYOTO, JAPAN
Y.
Takeyama
Graduate School of Pure and Applied Sciences, IBARAKI, TSUKUBA, JAPAN
The filtration of the Virasoro minimal series representations Mr,s(p, p') induced by the (1, 3)-primary field φ1,3(z) is studied. For 1 < p'/p < 2, a conjectural basis of Mr,s(p, p') compatible with the filtration is given by using monomial vectors in terms of the Fourier coeffcients of φ1,3(z). In support of this conjecture, we give two results. First, we establish the equality of the character of the conjectural basis vectors with the character of the whole representation space. Second, for the unitary series (p' = p + 1), we establish for each m the equality between the character of the degree m monomial basis and the character of the degree m component in the associated graded module gr(Mr,s(p, p+1)) with respect to the filtration defined by φ1,3(z).
Quantum theory
General
213
257
10.2977/prims/1210167327
http://www.ems-ph.org/doi/10.2977/prims/1210167327
Flops and Poisson Deformations of Symplectic Varieties
Yoshinori
Namikawa
Kyoto University, KYOTO, JAPAN
Algebraic geometry
Several complex variables and analytic spaces
General
259
314
10.2977/prims/1210167328
http://www.ems-ph.org/doi/10.2977/prims/1210167328
On ℚ-conic Bundles
Shigefumi
Mori
Kyoto University, KYOTO, JAPAN
Yuri
Prokhorov
Faculty of Mathematics, MOSCOW, RUSSIAN FEDERATION
A ℚ-conic bundle is a proper morphism from a threefold with only terminal singularities to a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We study the structure of ℚ-conic bundles near their singular fibers. One corollary to our main results is that the base surface of every ℚ-conic bundle has only Du Val singularities of type A (a positive solution of a conjecture by Iskovskikh). We obtain the complete classification of ℚ-conic bundles under the additional assumption that the singular fiber is irreducible and the base surface is singular.
Algebraic geometry
General
315
369
10.2977/prims/1210167329
http://www.ems-ph.org/doi/10.2977/prims/1210167329
Rigidity of Log Morphisms
Atsushi
Moriwaki
Kyoto University, KYOTO, JAPAN
Algebraic geometry
General
371
401
10.2977/prims/1210167330
http://www.ems-ph.org/doi/10.2977/prims/1210167330
The Orbibundle Miyaoka–Yau–Sakai Inequality and an Effective Bogomolov–McQuillan Theorem
Yoichi
Miyaoka
University of Tokyo, TOKYO, JAPAN
Orbibundle Miyaoka–Yau–Sakai inequality, effective bound of canonical degree
Let X be a minimal projective surface of general type defined over the complex numbers and let C ⊂ X be an irreducible curve of geometric genus g. Given a rational number α ∈ [0, 1], we construct an orbibundle Ẽα associated with the pair (X, C) and establish the Miyaoka–Yau–Sakai inequality for Ẽα. By varying the parameter α in the inequality, we derive several geometric consequences involving the “canonical degree” CKX of C. Specifically we prove the following two results. (1) If K2X is greater than the topological Euler number c2(X), then CKX is uniformly bounded from above by a function of the invariants g, K2X and c2(X)(an effective version of a theorem of Bogomolov–McQuillan). (2) If C is nonsingular, then CKX ≤ 3g − 3 + o(g) when g is large compared to K2X, c2(X) (an affrmative answer to a conjecture of McQuillan).
Algebraic geometry
Several complex variables and analytic spaces
General
403
417
10.2977/prims/1210167331
http://www.ems-ph.org/doi/10.2977/prims/1210167331
Flops Connect Minimal Models
Yujiro
Kawamata
University of Tokyo, TOKYO, JAPAN
A result by Birkar-Cascini–Hacon–McKernan together with the boundedness of length of extremal rays implies that different minimal models can be connected by a sequence of flops.
Algebraic geometry
General
419
423
10.2977/prims/1210167332
http://www.ems-ph.org/doi/10.2977/prims/1210167332
Divisorial Valuations via Arcs
Tommaso
de Fernex
University of Utah, SALT LAKE CITY, UNITED STATES
Lawrence
Ein
University of Illinois at Chicago, CHICAGO, UNITED STATES
Shihoko
Ishii
University of Tokyo, TOKYO, JAPAN
This paper shows a finiteness property of a divisorial valuation in terms of arcs. First we show that every divisorial valuation over an algebraic variety corresponds to an irreducible closed subset of the arc space. Then we define the codimension for this subset and give a formula of the codimension in terms of “relative Mather canonical class”. By using this subset, we prove that a divisorial valuation is determined by assigning the values of finite functions. We also have a criterion for a divisorial valuation to be a monomial valuation by assigning the values of finite functions.
Algebraic geometry
General
425
448
10.2977/prims/1210167333
http://www.ems-ph.org/doi/10.2977/prims/1210167333
Valuations and Plurisubharmonic Singularities
Sébastien
Boucksom
CNRS-Université Paris 6, PARIS CEDEX 05, FRANCE
Charles
Favre
École Polytechnique, Palaiseau Cedex, FRANCE
Mattias
Jonsson
University of Michigan, Ann Arbor, UNITED STATES
We extend to higher dimensions some of the valuative analysis of singularities of plurisubharmonic (psh) functions developed by the first two authors. Following Kontsevich and Soibelman we describe the geometry of the space V of all normalized valuations on C[x1 , . . . , xn] centered at the origin. It is a union of simplices naturally endowed with an affine structure. Using relative positivity properties of divisors living on modifications of Cn above the origin, we define formal psh functions on V, designed to be analogues of the usual psh functions. For bounded formal psh functions on V, we define a mixed Monge–Ampère operator which reflects the intersection theory of divisors above the origin of Cn. This operator associates to any (n − 1)-tuple of formal psh functions a positive measure of finite mass on V. Next, we show that the collection of Lelong numbers of a given germ u of a psh function at all infinitely near points induces a formal psh function û on V. When φ is a psh Hölder weight in the sense of Demailly, the generalized Lelong number νφ(u) equals the integral of û against the Monge–Ampère measure of φ^. In particular, any generalized Lelong number is an average of valuations. We also show how to compute the multiplier ideal of u and the relative type of u with respect to φ in the sense of Rashkovskii, in terms of û and φ^.
Several complex variables and analytic spaces
Commutative rings and algebras
Algebraic geometry
General
449
494
10.2977/prims/1210167334
http://www.ems-ph.org/doi/10.2977/prims/1210167334
Mordell–Weil Groups of a Hyperk¨hler a Manifold—A Question of F. Campana
Keiji
Oguiso
Osaka University, OSAKA, JAPAN
Among other things, we show that Mordell–Weil groups of finitely many different abelian fibrations of a hyperkähler manifold have essentially no relation, as its birational transformation. Precise definition of the terms “essentially no relation” will be given in Introduction.
Algebraic geometry
General
495
506
10.2977/prims/1210167335
http://www.ems-ph.org/doi/10.2977/prims/1210167335
Lattice Cohomology of Normal Surface Singularities
András
Némethi
Hungarian Academy of Sciences, BUDAPEST, HUNGARY
For any negative definite plumbed 3-manifold M we construct from its plumbed graph a graded ℤ[U]-module. This, for rational homology spheres, conjecturally equals the Heegaard–Floer homology of Ozsváth and Szabó, but it has even more structure. If M is a complex singularity link then the normalized Euler-characteristic can be compared with the analytic invariants. The Seiberg–Witten Invariant Conjecture of [16], [13] is discussed in the light of this new object.
Algebraic geometry
Several complex variables and analytic spaces
Manifolds and cell complexes
General
507
543
10.2977/prims/1210167336
http://www.ems-ph.org/doi/10.2977/prims/1210167336
On the Density of Unnormalized Tamagawa Numbers of Orthogonal Groups I
Norihiko
Hayasaka
Tohoku University, SENDAI, JAPAN
Akihiko
Yukie
Tohoku University, SENDAI, JAPAN
Number theory
General
545
607
10.2977/prims/1210167337
http://www.ems-ph.org/doi/10.2977/prims/1210167337
Functoriality in Resolution of Singularities
Edward
Bierstone
University of Toronto, TORONTO, ONTARIO, CANADA
Pierre
Milman
University of Toronto, TORONTO, ONTARIO, CANADA
Algorithms for resolution of singularities in characteristic zero are based on Hironaka’s idea of reducing the problem to a simpler question of desingularization of an “idealistic exponent” (or “marked ideal”). How can we determine whether two marked ideals are equisingular in the sense that they can be resolved by the same blowing-up sequences? We show there is a desingularization functor defined on the category of equivalence classes of marked ideals and smooth morphisms, where marked ideals are “equivalent” if they have the same sequences of “test transformations”. Functoriality in this sense realizes Hironaka’s idealistic exponent philosophy. We use it to show that the recent algorithms for desingularization of marked ideals of Włodarczyk and of Kollár coincide with our own, and we discuss open problems.
Algebraic geometry
Several complex variables and analytic spaces
General
609
639
10.2977/prims/1210167338
http://www.ems-ph.org/doi/10.2977/prims/1210167338
Simple Rational Polynomials and the Jacobian Conjecture
Lê Dũng
Tráng
ICTP, TRIESTE, ITALY
Algebraic geometry
General
641
659
10.2977/prims/1210167339
http://www.ems-ph.org/doi/10.2977/prims/1210167339
Elimination with Applications to Singularities in Positive Characteristic
Orlando
Villamayor U.
Universidad Autónoma de Madrid, MADRID, SPAIN
We present applications of elimination theory to the study of singularities over arbitrary fields. A partial extension of a function, defining resolution of singularities over fields of characteristic zero, is discussed here in positive characteristic.
Algebraic geometry
General
661
697
10.2977/prims/1210167340
http://www.ems-ph.org/doi/10.2977/prims/1210167340
Good Geometry on the Curve Moduli
Kefeng
Liu
Zhejiang University, HANGZHOU, CHINA
Xiaofeng
Sun
Lehigh University, BETHLEHEM, UNITED STATES
Shing-Tung
Yau
Harvard University, CAMBRIDGE, UNITED STATES
Algebraic geometry
Several complex variables and analytic spaces
Differential geometry
General
699
724
10.2977/prims/1210167341
http://www.ems-ph.org/doi/10.2977/prims/1210167341
3
Classification of Deformation Quantization Algebroids on Complex Symplectic Manifolds
Pietro
Polesello
Università di Padova, PADOVA, ITALY
A (holomorphic) deformation quantization algebroid over a complex symplectic manifold X is a stack locally equivalent to the ring of WKB operators, that is, microdifferential operators with an extra central parameter τ. In this paper, we will show that the (holomorphic) deformation quantization algebroids endowed with an anti-involution are classified by H2(X; k*X), where k∗ is a subgroup of the group of invertible series in ℂ[[τ−1]]. In the formal case, the analogous classification is given by H2(X; ℂX)[[ℏ]]odd , where one sets ℏ = τ−1.
Functional analysis
Category theory; homological algebra
Partial differential equations
General
725
748
10.2977/prims/1216238303
http://www.ems-ph.org/doi/10.2977/prims/1216238303
Conformally Invariant Systems of Differential Equations and Prehomogeneous Vector Spaces of Heisenberg Parabolic Type
L.
Barchini
Oklahoma State University, STILLWATER, UNITED STATES
Anthony
Kable
Oklahoma State University, STILLWATER, UNITED STATES
Roger
Zierau
Oklahoma State University, STILLWATER, UNITED STATES
Generalized Verma modules, Gyoja’s conjecture, covariant maps
Several systems of partial differential operators are associated to each complex simple Lie algebra of rank greater than one. Each system is conformally invariant under the given algebra. The systems so constructed yield explicit reducibility results for a family of scalar generalized Verma modules attached to the Heisenberg parabolic subalgebra of the given Lie algebra. Points of reducibility for such families lie in the union of several arithmetic progressions, possibly overlapping. For classical algebras, enough systems are constructed to account for the first point of reducibility in each progression. The relationship between these results and a conjecture of Akihiko Gyoja is explored.
Topological groups, Lie groups
Category theory; homological algebra
Partial differential equations
General
749
835
10.2977/prims/1216238304
http://www.ems-ph.org/doi/10.2977/prims/1216238304
Symmetric Crystals for gl∞
Naoya
Enomoto
Kyoto University, KYOTO, JAPAN
Masaki
Kashiwara
Kyoto University, KYOTO, JAPAN
Crystal bases, affine Hecke algebras, LLT conjecture
In the preceding paper, we formulated a conjecture on the relations between certain classes of irreducible representations of affine Hecke algebras of type B and symmetric crystals for gl∞. In the present paper, we prove the existence of the symmetric crystal and the global basis for gl∞.
Nonassociative rings and algebras
Group theory and generalizations
General
837
891
10.2977/prims/1216238305
http://www.ems-ph.org/doi/10.2977/prims/1216238305
On “M-Functions” Closely Related to the Distribution of L'/L-Values
Yasutaka
Ihara
Kyoto University, KYOTO, JAPAN
L-functions, density function, Euler product, Bessel functions
For each global field K, we shall construct and study two basic arithmetic functions, Mσ(K)(z) and its Fourier dual M~σ(K)(z), on ℂ parametrized by σ > 1/2. These functions are closely related to the density measure for the distribution of values on ℂ of the logarithmic derivatives of L-functions L(χ, s), where s is fixed, with Re(s) = σ, and χ runs over a natural infinite family of Dirichlet or Hecke characters on K. Connections with the Bohr–Jessen type value-distribution theories for the logarithms or (not much studied) logarithmic derivatives of ζK(σ + τi), where σ is fixed and τ varies, will also be briefly discussed.
Number theory
General
893
954
10.2977/prims/1216238306
http://www.ems-ph.org/doi/10.2977/prims/1216238306
On ℚ-conic Bundles, II
Shigefumi
Mori
Kyoto University, KYOTO, JAPAN
Yuri
Prokhorov
Faculty of Mathematics, MOSCOW, RUSSIAN FEDERATION
A ℚ-conic bundle germ is a proper morphism from a threefold with only terminal singularities to the germ (Z∌o) of a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. We obtain the complete classification of ℚ-conic bundle germs when the base surface germ is singular. This is a generalization of [MP08], which further assumed that the fiber over o is irreducible.
Algebraic geometry
General
955
971
10.2977/prims/1216238307
http://www.ems-ph.org/doi/10.2977/prims/1216238307
4
The Asymptotic Behavior of Singular Solutions of Some Nonlinear Partial Differential Equations in the Complex Domain
Sunao
Ōuchi
Sophia University, TOKYO, JAPAN
Singular solution, asymptotic behavior, complex partial differential equation, Mellin transform
Let u((t, x) ∈ ℂ × ℂd) be a solution of a nonlinear partial differential equation in a neighborhood of the origin, which is not necessarily holomorphic on {t = 0}. We study the asymptotic behavior of u((t, x) as t → 0 and give its asymptotic terms with remainder estimate of Gevrey type.
Partial differential equations
General
973
1026
10.2977/prims/1231263777
http://www.ems-ph.org/doi/10.2977/prims/1231263777
Beurling’s Theorem and Lp − Lq Morgan’s Theorem for Step Two Nilpotent Lie Groups
Sanjay
Parui
Indian Statistical Institute, KOLKATA, INDIA
Rudra
Sarkar
Indian Statistical Institute, KOLKATA, INDIA
Uncertainty principle, Beurling’s theorem, organ’s theorem, nilpotent Lie groups
We prove Beurling’s theorem and Lp − Lq Morgan’s theorem for step two nilpotent Lie groups. These two theorems together imply a group of uncertainty theorems.
Topological groups, Lie groups
Abstract harmonic analysis
General
1027
1056
10.2977/prims/1231263778
http://www.ems-ph.org/doi/10.2977/prims/1231263778
On the First Homology of the Groups of Foliation Preserving Diffeomorphisms for Foliations with Singularities of Morse Type
Kazuhiko
Fukui
Kyoto Sangyo University, KYOTO, JAPAN
Uncertainty principle, Beurling’s theorem, organ’s theorem, nilpotent Lie groups
Let ℚn be an n-dimensional Euclidean space and ℱφ be the foliation defined by levels of a Morse function φ : ℚn → ℚ. We determine the first homology of the identity component of the foliation preserving diffeomorphism group of (ℚn , ℱφ). Then we can apply it to the calculation of the first homology of the foliation preserving diffeomorphism groups for codimension one compact foliations with singularities of Morse type.
Global analysis, analysis on manifolds
Manifolds and cell complexes
General
1057
1068
10.2977/prims/1231263779
http://www.ems-ph.org/doi/10.2977/prims/1231263779
Discrete Tomography through Distribution Theory
Fumio
Hazama
Tokyo Denki University, TOKYO, JAPAN
Discrete tomography concerns with the problem of reconstruction of a function f on ℤn from various sums ft+v = Σx∈t+v f(x), v ∈ ℤn , where t is a fixed finite subset of ℤn. In this paper we focus on the structure of the set of functions satisfying ft+v = 0 for any v. Through the theory of distributions we deduce a dimension formula for the set of solutions. An intimate connection between the problem and certain types of PDE is revealed too, and it enables one to obtain an efficient algorithm, which constructs a solution from the corresponding PDE.
Difference and functional equations
Linear and multilinear algebra; matrix theory
Partial differential equations
General
1069
1095
10.2977/prims/1231263780
http://www.ems-ph.org/doi/10.2977/prims/1231263780
Vector Valued Hyperfunctions and Boundary Values of Vector Valued Harmonic and Holomorphic Functions
Paweł
Domański
Adam Mickiewicz University, POZNAN, POLAND
Michael
Langenbruch
Carl von Ossietzky Universität Oldenburg, Oldenburg, GERMANY
Vector valued hyperfunction, boundary values of vector valued holomorphic functions, boundary values of vector valued harmonic functions, partial differential operators on vector valued spaces of smooth functions, vector valued harmonic functions
We develop the theory of hyperfunctions with values in a locally convex nonnecessarily metrizable space E and find necessary conditions and sufficient conditions such that a reasonable theory of E-valued hyperfunctions exists. In particular, we show that it exists for various spaces of distributions but there is no such theory for the spaces of real analytic functions and distributions with compact support. We also show that vector valued hyperfunctions can be interpreted as boundary values of vector valued harmonic or holomorphic functions and, in many cases, as suitable cohomology groups.
Functional analysis
Real functions
Several complex variables and analytic spaces
Partial differential equations
1097
1142
10.2977/prims/1231263781
http://www.ems-ph.org/doi/10.2977/prims/1231263781
On the Profinite Regular Inverse Galois Problem
Anna
Cadoret
Université de Bordeaux I et C.N.R.S., TALENCE CEDEX, FRANCE
Given a field k, a k-curve X and a k-rational divisor t ⊂ X, we analyze the constraints imposed on X and t by the existence of abelian G-covers f : Y → X defined over k and unramified outside t. We show that these constraints produce an obstruction to the weak regular inverse Galois problem for a whole class of profinite groups - we call p-obstructed - when k is a finitely generated field of characteristic ≠ p.
Field theory and polynomials
Algebraic geometry
General
1143
1168
10.2977/prims/1231263782
http://www.ems-ph.org/doi/10.2977/prims/1231263782
Jacquet Modules of Principal Series Generated by the Trivial K-Type
Noriyuki
Abe
Hokkaido University, SAPPORO, JAPAN
We propose a new approach to the study of the Jacquet module of a HarishChandra module of a real semisimple Lie group. Using this method, we investigate the structure of the Jacquet module of a principal series representation generated by the trivial K-type.
Topological groups, Lie groups
General
1169
1197
10.2977/prims/1231263783
http://www.ems-ph.org/doi/10.2977/prims/1231263783
The Action of the Steenrod Algebra on the Cohomology of p-Compact Groups
Yutaka
Hemmi
Kochi University, KOCHI, JAPAN
Hirokazu
Nishinobu
Kochi University, KOCHI, JAPAN
Kuniyuki
Ogi
Anritsu Engineering Co., Ltd., KANAGAWA, JAPAN
p-compact group, cohomology operation, simple p-compact group
In the present paper, we determine the action of the Steenrod operations on the cohomology of simply connected p-compact groups with no p-torsion in the integral homologies for an odd prime p. To do so we study simple simply connected p-compact groups since any simply connected p-compact group with no p-torsion in the integral homology is a product of such p-compact groups.
Algebraic topology
Manifolds and cell complexes
General
1199
1218
10.2977/prims/1231263784
http://www.ems-ph.org/doi/10.2977/prims/1231263784
Brundan–Kazhdan–Lusztig and Super Duality Conjectures
Shun-Jen
Cheng
Academia Sinica, TAIPEI, TAIWAN
Weiqiang
Wang
University of Virginia, CHARLOTTESVILLE, UNITED STATES
Lie algebras, Lie superalgebras, representation theory, super duality
We formulate a general super duality conjecture on connections between parabolic categories O of modules over Lie superalgebras and Lie algebras of type A, based on a Fock space formalism of their Kazhdan–Lusztig theories which was initiated by Brundan. We show that the Brundan–Kazhdan–Lusztig (BKL) polynomials for gl(m|n) in our parabolic setup can be identified with the usual parabolic Kazhdan–Lusztig polynomials. We establish some special cases of the BKL conjecture on the parabolic category O of gl(m|n)-modules and additional results which support the BKL conjecture and super duality conjecture.
Nonassociative rings and algebras
Group theory and generalizations
General
1219
1272
10.2977/prims/1231263785
http://www.ems-ph.org/doi/10.2977/prims/1231263785