Local Transfer and Reducibility of Induced Representations of $p$-adic Groups of Classical Type

TL;DR

This paper studies when certain induced representations of p-adic classical groups are reducible, using local functorial transfers derived from global results, providing uniform criteria for reducibility points.

Contribution

It introduces a uniform approach to analyze reducibility of induced representations via local functorial transfers, connecting local and global representation theory.

Findings

Identifies reducibility points for induced representations of p-adic classical groups.

Establishes a connection between local reducibility and global functorial transfers.

Provides uniform criteria applicable across various groups and representations.

Abstract

We analyze reducibility points of representations of $p$-adic groups of classical type, induced from generic supercuspidal representations of maximal Levi subgroups, both on and off the unitary axis. We are able to give general, uniform results in terms of local functorial transfers of the generic representations of the groups we consider. The existence of the local transfers follows from global generic transfers that were established earlier.