A Local Trace Formula for the Generalized Shalika Model

TL;DR

This paper develops a local trace formula for generalized Shalika models, enabling the proof of a multiplicity formula for discrete series and revealing their relation to local exterior square L-functions.

Contribution

It introduces a local trace formula for generalized Shalika models and establishes a multiplicity formula for discrete series representations.

Findings

Multiplicities are constant over discrete Vogan L-packets.

Multiplicities are related to local exterior square L-functions.

The trace formula provides new tools for studying these models.

Abstract

We study local multiplicities associated to the so-called generalized Shalika models. By establishing a local trace formula for these kind of models, we are able to prove a multiplicity formula for discrete series. As a result, we can show that these multiplicities are constant over every discrete Vogan $L$-packet and that they are related to local exterior square $L$-functions.