Generic representations of GL(n) over a p-adic field distinguished by a maximal Levi subgroup

TL;DR

This paper classifies generic representations of GL(n) over a p-adic field that are distinguished by a maximal Levi subgroup, using inducing discrete series, advancing understanding of their structure.

Contribution

It provides a new classification framework for distinguished generic representations of GL(n) over p-adic fields based on inducing discrete series.

Findings

Classification of generic representations distinguished by maximal Levi subgroups

Connection between distinguished representations and inducing discrete series

Enhanced understanding of representation structure over p-adic fields

Abstract

Let $F$ be a non archimedean local field of characteristic zero, we give a classification of generic representations of $GL(n,F)$ distinguished by a maximal Levi subgroup, in terms of inducing discrete series.