- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 14:22:51
5
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=PRIMS&vol=53&iss=2&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
53
2017
2
Pull-back of Quasi-Log Structures
Osamu
Fujino
Osaka University, OSAKA, JAPAN
Quasi-log structures, log Fano pairs, fundamental groups
We prove that the pull-back of a quasi-log scheme by a smooth quasi-projective morphism has a natural quasi-log structure. We treat an application to log Fano pairs. This paper also contains a proof by Kento Fujita of the simple connectedness of log Fano pairs with only log canonical singularities.
Algebraic geometry
241
259
10.4171/PRIMS/53-2-1
http://www.ems-ph.org/doi/10.4171/PRIMS/53-2-1
$\Gamma$-Unitaries, Dilation and a Natural Example
Tirthankar
Bhattacharyya
Indian Institute of Science, BANGALORE, INDIA
Haripada
Sau
Indian Institute of Science, BANGALORE, INDIA
Symmetrized bidisk, spectral set, $\Gamma$-contraction, $\Gamma$-unitary, dilation
This note constructs an explicit normal boundary dilation for a commuting pair $(S,P)$ of bounded operators with the symmetrized bidisk $$\Gamma=\{(z_1+z_2,z_1z_2):|z_1|,|z_2| \leq 1\}$$ as a spectral set. Such explicit dilations had hitherto been constructed only in the unit disk [11], the unit bidisk [3] and in the tetrablock [6]. The dilation is minimal and unique under a suitable condition. This paper also contains a natural example of a $\Gamma$-isometry. We compute its associated fundamental operator.
Operator theory
Several complex variables and analytic spaces
Functional analysis
261
285
10.4171/PRIMS/53-2-2
http://www.ems-ph.org/doi/10.4171/PRIMS/53-2-2
Homogeneous Spaces of Nonreductive Type That Do Not Model Any Compact Manifold
Yosuke
Morita
University of Tokyo, TOKYO, JAPAN
Local model, $(G,X)$-structure, Clifford–Klein form, relative Lie algebra cohomology
We give necessary conditions for the existence of a compact manifold locally modeled on a given homogeneous space, which generalize some earlier results, in terms of relative Lie algebra cohomology. Applications include both reductive and nonreductive cases. For example, we prove that there does not exist a compact manifold locally modeled on a positive-dimensional coadjoint orbit of a real linear solvable algebraic group.
Differential geometry
Nonassociative rings and algebras
Topological groups, Lie groups
Manifolds and cell complexes
287
298
10.4171/PRIMS/53-2-3
http://www.ems-ph.org/doi/10.4171/PRIMS/53-2-3
Non-Cocycle-Conjugate E$_0$-Semigroups on Factors
Oliver
Margetts
Lancaster University, LANCASTER, UNITED KINGDOM
R.
Srinivasan
Chennai Mathematical Institute, SIRUSERI, INDIA
*-endomorphism, E$_0$-semigroup, CAR algebra, CCR algebra, quasi-free state, super-product system, type III factor, type II$_\infty$ factor
We investigate E$_0$-semigroups on general factors, which are not necessarily of type I or II$_1$. We show several families on the hyperfinite II$_\infty$ factor, which arises as tensor products, consists of mutually non-cocycle-conjugate E$_0$-semigroups. Using CCR representations associated with quasi-free states, we exhibit, for the first time, uncountable families consisting of mutually non-cocycle-conjugate E$_0$-semigroups on all type III$_\lambda$ factors, for $\lambda \in (0,1]$. They are not cocycle conjugate to the E$_0$-semigroups constructed using CAR representations.
Functional analysis
299
336
10.4171/PRIMS/53-2-4
http://www.ems-ph.org/doi/10.4171/PRIMS/53-2-4
A Weak Converse Theorem for Degree 2 $L$-Functions with Conductor 1
Jerzy
Kaczorowski
Adam Mickiewicz University, POZNAN, POLAND
Alberto
Perelli
Università di Genova, GENOVA, ITALY
$L$-functions, Selberg class, converse theorems, cusp forms
We show that every normalized function of degree 2 and conductor 1 in the extended Selberg class has real coe fficients, and certain invariants agree with those of the $L$-functions of cusp forms for the full modular group. The result may therefore be regarded as a weak converse theorem in such a general setting.
Number theory
337
347
10.4171/PRIMS/53-2-5
http://www.ems-ph.org/doi/10.4171/PRIMS/53-2-5