Caract\`eres de repr\'esentations de niveau 0

TL;DR

This paper computes the characters of all finite-length, depth-zero smooth representations of p-adic groups, showing they are linear combinations of weighted orbital integrals at strongly regular semi-simple points.

Contribution

It extends the understanding of representation characters by explicitly expressing them as weighted orbital integrals using advanced resolutions.

Findings

Characters are linear combinations of weighted orbital integrals.

Explicit formulas for characters at strongly regular semi-simple points.

Connections between representation theory and orbital integrals are clarified.

Abstract

Using the results of Meyer and Solleveld on the resolutions of Schneider and Stuhler, we compute the character of every smooth representation of finite length and of depht 0 of a p-adic group. We prove that, in every strongly regular semi-simple point, the character is equal to some linear combination of weighted orbital integrals.