Parity of the Langlands parameters of conjugate self-dual representations of GL(n) and the local Jacquet-Langlands correspondence

TL;DR

This paper investigates the parity of Langlands parameters for conjugate self-dual supercuspidal representations of GL(n) over non-archimedean local fields, using the local Jacquet-Langlands correspondence to extend previous results.

Contribution

It provides a partial generalization of known results on self-dual cases to conjugate self-dual representations via the Jacquet-Langlands correspondence.

Findings

Determines the parity of Langlands parameters for conjugate self-dual representations.

Extends previous results from self-dual to conjugate self-dual cases.

Uses the local Jacquet-Langlands correspondence as a key tool.

Abstract

We determine the parity of the Langlands parameter of a conjugate self-dual supercuspidal representation of GL(n) over a non-archimedean local field by means of the local Jacquet-Langlands correspondence. It gives a partial generalization of a previous result on the self-dual case by Prasad and Ramakrishnan.