Highest weight modules and \(b\)-functions of semi-invariants

DOI10.2977/prims/1195165904zbMath0821.22006OpenAlexW2069241085MaRDI QIDQ1343235

Akihiko Gyoja

Publication date: 1 February 1995

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195165904

zbMATH Keywords

micro-local structureholonomy diagramsirreducibility of generalized Verma modulesroots of \(b\)-functions of semi-invariants

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Homogeneous spaces and generalizations (14M17) Universal enveloping (super)algebras (17B35) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (11)

On the regularity of prehomogeneous vector spaces ⋮ Integral geometry for \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {D}}$\end{document}‐modules on dual flag manifolds and generalized Verma modules ⋮ On the reducibility of scalar generalized Verma modules associated to maximal parabolic subalgebras ⋮ Algebraic analysis of scalar generalized Verma modules of Heisenberg parabolic type I: \(\mathsf{A}_{n}\)-series ⋮ On the meromorphic extension of the spherical functions on noncompactly causal symmetric spaces ⋮ Generalized Verma modules, \(b\)-functions of semi-invariants and duality for twisted \(D\)-modules on generalized flag manifolds ⋮ The homomorphisms between scalar generalized Verma modules associated to maximal parabolic subalgebras ⋮ Quantum \(b\)-functions of prehomogeneous vector spaces of commutative parabolic type ⋮ Desingularization of Schubert varieties and orbit closures of prehomogeneous vector spaces of commutative parabolic type ⋮ The \(b\)-functions for prehomogeneous vector spaces of commutative parabolic type and universal generalized Verma modules ⋮ Certain unipotent representations of finite Chevalley groups and Picard–Lefschetz monodromy

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