Almost special representations of Weyl groups

TL;DR

This paper introduces a subset of irreducible Weyl group representations associated with a two-sided cell, linking special and constructible representations through a canonical bijection.

Contribution

It defines a new subset of irreducible representations of Weyl groups that connects special and constructible representations in a canonical way.

Findings

Established a subset $A_c$ containing the special representation

Proved a canonical bijection between $A_c$ and constructible representations

Enhanced understanding of the structure of Weyl group representations

Abstract

Let $c$ be the family of irreducible representations of a Weyl group $W$ corresponding to a two-sided cell of $W$. We define a subset $A_c$ of $c$ which contains the special representation of $W$ in $c$ and is in canonical bijection with the set of constructible representations of $W$ attached to $c$.