Depth-zero Supercuspidal L-packets and Their Stability

 

From Annals of Mathematics 169 No. 3 (2009), 795-901

By Mark Reeder, Professor of Mathematics and Stephen DeBacker, Professor of Mathematics, University of Michigan

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.

Depth-zero Supercuspidal L-packets and Their Stability

 

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