Antispecial representations of Weyl groups

TL;DR

This paper introduces antispecial representations of Weyl groups, establishing a bijection with constructible representations and describing their explicit structure and associated graph.

Contribution

It defines a new class of irreducible representations called antispecial, linking them to constructible representations and providing explicit descriptions and graph structures.

Findings

Antispecial representations are in bijection with constructible representations.

An explicit description of antispecial representations for each case is provided.

A graph structure on antispecial representations is introduced and analyzed.

Abstract

Let W be a Weyl group. We define a class of irreducible representations of W that we call antispecial. They are in bijection with the constructible representations of W. We define an oriented graph structure on the set of antispecial representations or equivalently on the set of constructible representations of W. We describe explicitly the antispecial representations in each case. Section 2 has been modified.