Representations distinguished by pairs of exceptional representations and a conjecture of Savin

TL;DR

This paper characterizes distinguished representations of GL(n) as quotients of tensor products of exceptional representations, completing a conjecture of Savin by linking spherical distinguished representations to classical group lifts.

Contribution

It provides a complete characterization of distinguished principal series representations and proves Savin's conjecture relating these to classical group lifts.

Findings

Characterization of distinguished principal series representations.

Completion of Savin's conjecture on spherical distinguished representations.

Connection established between distinguished representations and classical group lifts.

Abstract

We study representations of GL(n) appearing as quotients of a tensor of exceptional representations, in the sense of Kazhdan and Patterson. Such representations are called distinguished. We characterize distinguished principal series representations in terms of their inducing data. In particular, we complete the proof of a conjecture of Savin, relating distinguished spherical representations to the image of the tautological lift from a suitable classical group.