Interview with Mark Reeder on Depth-zero supercuspidal L-packets and their stability, by Mark Reeder and Stephen DeBacker

Abstract

In this article Professors DeBacker and Reeder verify the local Langlands correspondence for pure inner forms of unramified p-adic groups and tame Langlands parameters in "general position". For each such parameter, the authors explicitly construct, in a natural way, a finite set ("L-packet") of depth-zero supercuspidal representations of the appropriate p-adic group, and they verify some expected properties of this L-packet. In particular, the authors prove, with some conditions on the base field, that the appropriate sum of characters of the representations in the author's L-packet is stable.