An inversion formula for relative kazhdan—lusztig polynomials

DOI10.1080/00927879008823919zbMath0723.20022OpenAlexW2091679958MaRDI QIDQ3211524

J. Matthew Douglass

Publication date: 1990

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927879008823919

zbMATH Keywords

inversion formulaHecke algebraCoxeter systemleft cell modules\({\mathcal H}\)-modulesrelative Kazhdan-Lusztig polynomials

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05)

Related Items (23)

Unnamed Item ⋮ Parabolic Kazhdan-Lusztig polynomials of type \(-1\) for quasi-minuscule quotients ⋮ An inversion formula for some Fock spaces ⋮ Dual canonical bases and Kazhdan-Lusztig polynomials ⋮ A geometric Steinberg formula ⋮ Singular Rouquier complexes ⋮ \(\imath\)Schur duality and Kazhdan-Lusztig basis expanded ⋮ Irreducible representations of \(\mathrm{GL}_n (\mathbb{C})\) of minimal Gelfand-Kirillov dimension ⋮ Duality in parabolic set up for questions in Kazhdan-Lusztig theory ⋮ Monoid Hecke algebras ⋮ A twisted duality for parabolic Kazhdan-Lusztig \(R\)-polynomials ⋮ Kazhdan-Lusztig-Polynome und eine Kombinatorik für Kipp-Moduln ⋮ On the dual canonical and Kazhdan-Lusztig bases and 3412-, 4231-avoiding permutations ⋮ Some properties of inverse weighted parabolic Kazhdan-Lusztig polynomials ⋮ An inversion formula for induced Kazhdan-Lusztig polynomials and duality of \(W\)-graphs. ⋮ Reductive groups, the loop Grassmannian, and the Springer resolution ⋮ Bar operators for quasiparabolic conjugacy classes in a Coxeter group. ⋮ \(W\)-graph ideals and duality ⋮ Equivariant \(K\)-theory of generalized Steinberg varieties ⋮ A Kazhdan-Lusztig algorithm for Whittaker modules ⋮ IrreducibleW-Graphs for TypeD₄andD₅ ⋮ An Inversion Formula for -Relative Kazhdan–Lusztig Polynomials ⋮ Quiver Schur algebras for linear quivers

Cites Work

• On Lusztig's isomorphism theorem for Hecke algebras
• On some geometric aspects of Bruhat orderings. II: The parabolic analogue of Kazhdan-Lusztig polynomials
• Representations of Coxeter groups and Hecke algebras
• Some characterizations of Bruhat ordering on a Coxeter group and determination of the relation Möbius function

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