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European Mathematical Society Publishing House
2024-03-29 11:11:18
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https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=44&iss=3&update_since=2024-03-29
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
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European Mathematical Society Publishing House
Zuerich, Switzerland
© Research Institute for Mathematical Sciences, Kyoto University
44
2008
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