A local trace formula for the generalized Shalika model

Abstract

We study a local multiplicity problem related to so-called generalized Shalika models. By establishing a local trace formula for these kinds of models, we are able to prove a multiplicity formula for discrete series. As a result, we can show that these multiplicities are, for discrete series, invariant under the local Jacquet–Langlands correspondence and are related to local exterior square $L$-functions.