An inversion formula for the Kazhdan-Lusztig polynomials for affine Weyl groups

DOI10.1016/S0001-8708(86)80008-1zbMath0598.20044MaRDI QIDQ1079662

Henning Haahr Andersen

Publication date: 1986

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

inversion formulaCoxeter groupaffine Weyl grouplength function

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05)

Related Items

Jantzen's filtrations of Weyl modules ⋮ Unnamed Item ⋮ On the Frobenius direct image of the structure sheaf of a homogeneous projective variety ⋮ Twisting functors on 𝒪 ⋮ Equivariant localization of \(\overline D\)-modules on the flag variety of the symplectic group of degree 4. ⋮ Extensions of modules for infinitesimal algebraic groups ⋮ Some non-trivial Kazhdan-Lusztig coefficients of an affine Weyl group of type \(\widetilde A_n\). ⋮ On stable decomposition patterns of weyl modules ⋮ Socle series of cohomology groups of line bundles on \(G/B\) ⋮ Extensions between simple modules for Frobenius kernels ⋮ Kazhdan-Lusztig-Polynome und eine Kombinatorik für Kipp-Moduln ⋮ Filtrations of cohomology modules for Chevalley groups ⋮ On the Kazhdan-Lusztig polynomials for affine Weyl groups ⋮ Kazhdan-Lusztig coefficients for an affine Weyl group of type \(\widetilde B_2\). ⋮ Cohomology of line bundles on the flag variety for type \(G_2\). ⋮ Loewy Series of Certain Indecomposable Modules for Frobenius Subgroups ⋮ Extensions of simple modules for finite Chevalley groups ⋮ Reductive groups, the loop Grassmannian, and the Springer resolution ⋮ Computation of Kazhdan-Lusztig polynomials and some applications to finite groups ⋮ Cohomology of infinitesimal algebraic groups ⋮ Semistandard filtrations in highest weight categories. ⋮ Abstract Kazhdan-Lusztig theories ⋮ Balanced semisimple filtrations for tilting modules ⋮ Some new examples in 1-cohomology

Cites Work

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• Cohomology of G/B in characteristic p
• Irreducible characters of semisimple Lie groups. II: The Kazhdan-Lusztig conjectures
• Hecke algebras and Jantzen's generic decomposition patterns
• Kazhdan-Lusztig conjecture and holonomic systems
• On the structure of the cohomology of line bundles on G/B
• Representations of Coxeter groups and Hecke algebras
• Rational and generic cohomology
• The strong linkage principle.
• Towards the Kazhdan-Lusztig conjecture