Local Jacquet-Langlands correspondences for simple supercuspidal   representations
  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. 
Naoki Imai and Takahiro Tsushima
math.NT math.RT