Local Jacquet-Langlands correspondences for simple supercuspidal representations

TL;DR

This paper describes the local Jacquet-Langlands correspondence for simple supercuspidal representations using type theory, and shows the invariance of endo-classes under this correspondence.

Contribution

It provides a new description of the correspondence for simple supercuspidal representations and proves endo-class invariance.

Findings

Endo-classes are invariant under the correspondence.

A description of the correspondence via type theory.

Clarification of the structure of simple supercuspidal representations.

Abstract

We give a description of the local Jacquet-Langlands correspondence for simple supercuspidal representations via type theory. As a consequence, we show that the endo-classes for such representations are invariant under the local Jacquet-Langlands correspondence.