Special representations of Weyl groups: a positivity property

TL;DR

This paper demonstrates that certain irreducible representations of the asymptotic Hecke algebra linked to special Weyl group representations possess a basis with notable positivity properties.

Contribution

It introduces a new basis with strong positivity properties for irreducible representations of the asymptotic Hecke algebra associated with special Weyl group representations.

Findings

Existence of a basis with strong positivity properties.

Application to irreducible representations of the asymptotic Hecke algebra.

Enhanced understanding of representation structure.

Abstract

We show that the irreducible representation of the asymptotic Hecke algebra corresponding to a special representation of a Weyl group admits a basis with strong positivity properties.