Twisted character formula for toral supercuspidal representations

TL;DR

This paper derives an explicit formula for twisted characters of toral supercuspidal representations in p-adic groups, including quasi-split cases with involutions, advancing understanding of their harmonic analysis.

Contribution

It provides a new explicit twisted character formula for toral supercuspidal representations, especially in quasi-split groups with involutions, under specific technical assumptions.

Findings

Explicit twisted character formula derived

Includes quasi-split groups with involutions

Enhances harmonic analysis of p-adic groups

Abstract

We establish an explicit formula for twisted Harish-Chandra characters of toral supercuspidal representations of p-adic reductive groups under several technical assumptions. Our setup especially includes the case of a quasi-split group equipped with an involution.