Asymptotics of matrix coefficients, perverse sheaves, and Jacquet modules

DOI10.1007/BF01458580zbMath0743.22011MaRDI QIDQ5905513

Luis G. Casian

Publication date: 27 September 1992

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/164130

zbMATH Keywords

homologyflag varietyhomology groupsBorel subalgebranilradicalperverse sheavesBGG categoryHarish-Chandra moduleholonomic \(D\)-moduleslocalization theoryconnected semisimple algebraic groupasymptotics of matrix coefficientsKazhdan-Lusztig conjecturesantidominant weight spacegeneralized Jacquet modulessolution complex

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Grassmannians, Schubert varieties, flag manifolds (14M15) Semisimple Lie groups and their representations (22E46) Homological methods in Lie (super)algebras (17B55) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Sheaves and cohomology of sections of holomorphic vector bundles, general results (32L10) de Rham cohomology and algebraic geometry (14F40)

Cites Work

• Characters, asymptotic and n-homology of Harish-Chandra modules
• Asymptotic behavior of matrix coefficients of admissible representations
• Intersection homology. II
• Primitive ideals and representations
• Complex geometry and the asymptotics of Harish-Chandra modules for real reductive Lie groups. II
• Vanishing theorems for Lie algebra cohomology and the cohomology of discrete subgroups of semisimple Lie groups
• Kazhdan-Lusztig conjecture and holonomic systems
• On the maximally overdetermined system of linear differential equations. I
• Irreducible characters of semisimple Lie groups. III: Proof of Kazhdan-Lusztig conjecture in the integral case
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