Distinction of the Steinberg representation and a conjecture of Prasad and Takloo-Bighash

TL;DR

This paper proves a conjecture related to the Steinberg representation for inner forms of the general linear group over non-archimedean local fields, advancing understanding in representation theory.

Contribution

It confirms a conjecture of Prasad and Takloo-Bighash specifically for Steinberg representations of inner forms of GL over non-archimedean fields.

Findings

Proof of the conjecture for Steinberg representations

Clarification of the distinction of the Steinberg representation

Advancement in the theory of inner forms of GL

Abstract

We prove a conjecture of Prasad and Takloo-Bighash for discrete series of inner forms of the general linear group over a non archimedean local field, in the case of Steinberg representations.