A bar operator for involutions in a Coxeter group

Abstract

In [LV] the authors defined a Hecke algebra action and a bar involution on a vector space spanned by the involutions in a Weyl group. In this paper we give a new definition of the Hecke algebra action and the bar operator which, unlike the one in [LV], is completely elementary (does not use geometry) and in particular it makes sense for an arbitrary Coxeter group.

40 pages. This version has some additional material compared to the earlier one

References in corpus (2)

• Hecke algebras and involutions in Weyl groups
• Involutions in Coxeter groups

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