Formal degrees of unipotent discrete series representations and the exotic Fourier transform

Abstract

We introduce a notion of elliptic fake degrees for unipotent elliptic representations of a semisimple p-adic group. We conjecture, and verify in some cases, that the relation between the formal degrees of unipotent discrete series representations of a semisimple p-adic group and the elliptic fake degrees is given by the exotic Fourier transform matrix introduced by Lusztig in the study of representations of finite groups of Lie type.

32 pages; v2: added references, minor corrections

Cited by in corpus (2)

• A uniform classification of discrete series representations of affine Hecke algebras
• Topological K-theory of affine Hecke algebras