From Annals of Mathematics 169 No. 3 (2009), 795901By 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 padic groups and tame Langlands parameters in “general position”. For each such parameter, the authors explicitly construct, in a natural way, a finite set (“Lpacket”) of depthzero supercuspidal representations of the appropriate padic group, and they verify some expected properties of this Lpacket. 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 Lpacket is stable.
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