Involutions in Weyl groups and nil-Hecke algebras

TL;DR

This paper explores the action of the Iwahori-Hecke algebra on involutions in Coxeter groups, providing a simplified description at a specific parameter value, advancing understanding of algebraic structures related to Weyl groups.

Contribution

It introduces a simplified description of the Iwahori-Hecke algebra action on involutions at parameter zero, building on previous work.

Findings

Specialization at parameter zero simplifies the algebraic action.

Provides explicit description of the action on involutions.

Enhances understanding of Weyl group related algebraic structures.

Abstract

In a previous article we have defined an action of the Iwahori-Hecke algebra of a Coxeter group W on a free module with basis indexed by the involutions in W. In this paper we show that the specialization of this action at the parameter 0 has a simple description.