Combinatorial properties of the Kazhdan-Lusztig \(R\)-polynomials for \(S_ n\)

DOI10.1006/aima.1996.1607zbMath0870.20011OpenAlexW2027607277MaRDI QIDQ1354673

Francesco Brenti

Publication date: 21 July 1997

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

Full work available at URL: https://doi.org/10.1006/aima.1996.1607

zbMATH Keywords

Hecke algebrassymmetric groupsCoxeter groupsKazhdan-Lusztig polynomialsclosed formularecursion formulaBruhat orders\(R\)-polynomialsproducts of polynomials

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30)

Related Items

A combinatorial formula for Kazhdan-Lusztig polynomials ⋮ Combinatorial properties of the Temperley-Lieb algebra of a Coxeter group. ⋮ Kazhdan-Lusztig \(R\)-polynomials of permutations containing a 231 or 312 pattern ⋮ Kazhdan-Lusztig immanants and products of matrix minors ⋮ A decomposition of \(R\)-polynomials and Kazhdan-Lusztig polynomials ⋮ Proof of two conjectures of Brenti and Simion on Kazhdan-Lusztig polynomials ⋮ On 1234-nesting Kazhdan–Lusztig R-polynomials for the symmetric group ⋮ Cyclic sieving, promotion, and representation theory ⋮ Explicit formulae for some Kazhdan-Lusztig \(R\)-polynomials. ⋮ Non-negativity properties of \(R\)-polynomials ⋮ Formulas for multi-parameter classes of Kazhdan-Lusztig polynomials in \({\mathfrak S}(n)\) ⋮ Unnamed Item ⋮ A Simple Product Formula for Certain Kazhdan-LusztigR-Polynomials ⋮ Explicit formulae for some Kazhdan-Lusztig polynomials ⋮ Kazhdan-Lusztig and \(R\)-polynomials from a combinatorial point of view. ⋮ Boolean elements in Kazhdan-Lusztig theory.

Cites Work

• A combinatorial setting for questions in Kazhdan-Lusztig theory
• Posets, regular CW complexes and Bruhat order
• On some geometric aspects of Bruhat orderings. I: A finer decomposition of Bruhat cells
• The Kazhdan-Lusztig cells in certain affine Weyl groups
• Moduln mit einem höchsten Gewicht
• Bruhat order of Coxeter groups and shellability
• Representations of Coxeter groups and Hecke algebras
• Combinatorics and intersections of Schubert varieties
• Some characterizations of Bruhat ordering on a Coxeter group and determination of the relation Möbius function
• SCHUBERT CELLS AND COHOMOLOGY OF THE SPACESG/P
• Möbius inversion for the Bruhat ordering on a Weyl group
• Introduction to Lie Algebras and Representation Theory
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item