Twisted Harish–Chandra Sheaves and Whittaker Modules: The Nondegenerate Case

DOI10.1007/978-3-319-09934-7_7zbMath1322.22018OpenAlexW1781329069MaRDI QIDQ5265190

Wolfgang Soergel, Dragan Milicic

Publication date: 22 July 2015

Published in: Developments and Retrospectives in Lie Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-09934-7_7

zbMATH Keywords

D-modulesWhittaker moduleslocalization of representations

Mathematics Subject Classification ID

Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items (15)

Four examples of Beilinson–Bernstein localization ⋮ A structure theorem for Harish-Chandra bimodules via coinvariants and Golod rings ⋮ Contravariant pairings between standard Whittaker modules and Verma modules ⋮ Kazhdan-Lusztig algorithm for Whittaker modules with arbitrary infinitesimal characters ⋮ Kostant's problem for Whittaker modules ⋮ Whittaker categories and the minimal nilpotent finite \(W\)-algebras for \(\mathfrak{sl}_{n+1}\) ⋮ Generalized Verma modules over \(\mathfrak{sl}_{n + 2}\) induced from \(\mathcal{U}(\mathfrak{h}_n)\)-free \(\mathfrak{sl}_{n + 1}\)-modules ⋮ New simple modules for the Heisenberg-Virasoro algebra ⋮ Contravariant forms on Whittaker modules ⋮ Whittaker modules for classical Lie superalgebras ⋮ Projective and Whittaker functors on category \(\mathcal{O}\) ⋮ Simple restricted modules for the Heisenberg-Virasoro algebra ⋮ A Kazhdan-Lusztig algorithm for Whittaker modules ⋮ Intermediate extensions and crystalline distribution algebras ⋮ Arakawa-Suzuki functors for Whittaker modules

Cites Work

• Localization and standard modules for real semisimple Lie groups. I: The duality theorem
• On modules induced from Whittaker modules
• On Whittaker vectors and representation theory
• The composition series of modules induced from Whittaker modules
• Wild Harmonic Bundles and Wild Pure Twistor D-modules
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