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 -functions.
"A local trace formula for the generalized Shalika model." Duke Math. J. 168 (7) 1303 - 1385, 15 May 2019. https://doi.org/10.1215/00127094-2018-0064