On the characters of unipotent representations of a semisimple p-adic group

TL;DR

This paper computes the characters of unipotent representations of split semisimple p-adic groups at specific regular elements, enhancing understanding of their structure and behavior.

Contribution

It provides explicit character formulas for unipotent representations of semisimple p-adic groups at compact very regular elements, a novel calculation in the field.

Findings

Explicit character formulas for unipotent representations

Character values at compact very regular elements computed

Enhanced understanding of representation structure

Abstract

Let G be a semisimple almost simple algebraic group defined and split over a nonarchimedean local field K and let V be a unipotent representation of G(K) (for example, an Iwahori-spherical representation). We calculate the character of V at compact very regular elements of G(K) at compact very regular elements of G(K).