Transfert du pseudo-coefficient de Kottwitz et formules de caractere pour la serie discrete de GL(N) d'un corps local

TL;DR

This paper constructs explicit pseudo-coefficients for discrete series representations of GL(N,F) using Bushnell-Kutzko types and Henniart's idea, leading to new formulas for Harish-Chandra characters at elliptic elements.

Contribution

It introduces a novel method for constructing pseudo-coefficients for discrete series of GL(N,F) and derives explicit character formulas at elliptic elements.

Findings

Explicit pseudo-coefficients constructed for discrete series

New formulas for Harish-Chandra characters at elliptic elements

Application of Bushnell-Kutzko types and Henniart's idea

Abstract

Let G be the group GL(N,F), where F is a non-archimedean locally compact field. Using Bushnell and Kutzko's simple types, as well as an original idea of Henniart's, we construct explicit pseudo-coefficients for the discrete series representations of G. As an application we deduce new formulas for the value of the Harish-Chandra character of certain such representations at certain elliptic regular elements.