Supercuspidal characters of reductive p-adic groups

TL;DR

This paper computes explicit formulas for supercuspidal characters of reductive p-adic groups, expanding understanding of their structure and providing tools for further representation theory analysis.

Contribution

It introduces explicit character formulas for supercuspidal representations constructed via Yu's method under certain conditions, linking them to orbital integrals and smaller group characters.

Findings

Explicit character formulas for supercuspidal representations.

Connection between characters and orbital integrals.

Descriptions of signs and cardinalities in formulas.

Abstract

We compute the characters of many supercuspidal representations of reductive p-adic groups. Specifically, we deal with representations that arise via Yu's construction from data satisfying a certain compactness condition. Each character is expressed in terms of a depth-zero character of a smaller group, the (linear) characters appearing in Yu's construction, Fourier transforms of orbital integrals, and certain signs and cardinalities that are described explicitly in terms of the datum associated to the representation and of the element at which the character is evaluated.