Characters of some simple supercuspidal representations on split tori

TL;DR

This paper computes the characters of simple supercuspidal representations of SL(2,F) and SL(3,F) on split tori, providing explicit character formulas for these representations over non-Archimedean local fields.

Contribution

It explicitly calculates the characters of simple supercuspidal representations on split tori for SL(2,F) and SL(3,F), expanding understanding of these representations.

Findings

Explicit character formulas for SL(2,F) and SL(3,F) supercuspidal representations

Character values on split tori are determined

Provides tools for further harmonic analysis on p-adic groups

Abstract

In this paper, we compute the characters of the simple supercuspidal representations of SL(2,F) and SL(3,F) on split tori. Here, F is an arbitrary non-Archimedean local field of characteristic zero.