Hecke algebras and involutions in Coxeter groups

G. Lusztig, D. A. Vogan Jr

Published 2013-12-11, updated 2014-05-28Version 3

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 $M$.