PARITY OF THE LANGLANDS PARAMETERS OF CONJUGATE SELF-DUAL REPRESENTATIONS OF AND THE LOCAL JACQUET–LANGLANDS CORRESPONDENCE

Abstract

We determine the parity of the Langlands parameter of a conjugate self-dual supercuspidal representation of$\text{GL}(n)$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.