Antispecial representations of Weyl groups

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.