On the Steinberg character of a reductive p-adic group

TL;DR

This paper generalizes the construction of the Steinberg tempered character for connected reductive p-adic groups and proves its invariance under weak Jacquet module restriction, extending known finite group results.

Contribution

It introduces a generalized construction of the Steinberg tempered character for p-adic groups and establishes its invariance properties.

Findings

Steinberg character construction extended to p-adic groups

Proved invariance under weak Jacquet module restriction

Analogous results to finite reductive groups

Abstract

The aim of this paper is to give generalizationof the constructionof the Steinberg tempered character on a connected reductive p-adic group. We prove that this character is invariant by the weak restriction of the Jacquet module by analogy to finite reductive groups.