Hecke algebras and involutions in Coxeter groups

2013/12/11 by G. Lusztig, Lusztig, G., D. A. Vogan +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1312.3237

openalex publication_date 2013/12/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let W be a Coxeter group and let M be the free Z[v,v^-1]-module with basis indexed by the involutions of W. We show how recent results of Elias and Williamson on Soergel bimodules can be used to give an alternative definition of an action of the Hecke algebra of W on M.

Related

• Involutions in Weyl groups and nil-Hecke algebras
• Involutions in Coxeter groups
• An involution based left ideal in the Hecke algebra
• A bar operator for involutions in a Coxeter group
• Asymptotic Hecke algebras and involutions