Formule de caract\`ere pour la s\'erie discr\`ete de GL(N). Guide de l'utilisateur pour typistes

TL;DR

This paper provides formulas for characters of the discrete series representations of GL(N) over non-archimedean local fields, aiding specialists in applying Bushnell-Kutzko type theory.

Contribution

It establishes explicit character formulas for the discrete series of GL(N) over non-archimedean fields, expanding the tools available for representation theory analysis.

Findings

Derived explicit character formulas for discrete series of GL(N)

Enhanced understanding of Type Theory applications

Supported advanced research in non-archimedean representation theory

Abstract

Ces notes en fran\c{c}ais sont un r\'esum\'e de la pr\'epublication arXiv:1402.2501, o\`u en collaboration avec Peter Schneider, nous \'etablissons des formules de caract\`ere pour la s\'erie discr\`ete de GL(N) d'un corps local non archim\'edien. Elles s'adressent \`a un public de sp\'ecialistes suffisamment \`a l'aise avec les notations et les concepts de la Th\'eorie des Types de Bushnell et Kutzko. These notes, written in french, are a summary of the preprint arXiv:1402.2501, where in collaboration with Peter Schneider, we establish character formulas for the discrete series of GL(N) of a non archimedean local field. They are written for specialists who feel sufficiently confortable with the notation and concept of Type Theory as developped by Bushnell and Kutzko.