An orthogonality relation for spherical characters of supercuspidal representations

TL;DR

This paper establishes an orthogonality relation for spherical characters of supercuspidal representations within the context of Galois pairs, contributing to the understanding of their harmonic analysis.

Contribution

It introduces a new orthogonality relation for spherical characters of supercuspidal representations in Galois pairs, expanding theoretical knowledge.

Findings

Spherical characters satisfy an orthogonality relation.

The result applies specifically to Galois pairs.

Enhances understanding of harmonic analysis on p-adic groups.

Abstract

In this note, we show that, in the setting of Galois pairs, the spherical characters of unitary supercuspidal representations satisfy an orthogonality relation.