Distinguished principal series representations for GLn over a p-adic field

TL;DR

This paper characterizes distinguished irreducible principal series representations of GLn over p-adic fields using inducing data, providing a counter-example to a prior conjecture about distinction.

Contribution

It offers a new description of distinguished principal series representations and challenges a previous conjecture by Jacquet.

Findings

Provides explicit description of distinguished principal series representations.

Constructs a counter-example to Jacquet's conjecture on distinction.

Enhances understanding of representation theory over p-adic fields.

Abstract

In the following article, we give a description of the distingushed irreducible principal series representations of the general linear group over a p-adic field in terms of inducing datum. This provides a counter-example to a conjecture of Jacquet about distinction (Conjecture 1 in U.K Anandavardhanan, "Distinguished non-Archimedean representations ", Proc. Hyderabad Conference on Algebra and Number Theory, 2005, 183-192).