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MR2276772 (2008c:22014) 22E50 (20G25 22E35)
Kim, Ju-Lee (1-ILCC)
Supercuspidal representations: an exhaustion theorem.
J. Amer. Math. Soc. 20 (2007), no. 2, 273320 (electronic).
Let k be a p-adic field and G the group of k-rational points of a connected reductive group G
defined over k. Assume that G is split over a finite tamely ramified extension E of k. In [J. Amer.
Math. Soc. 14 (2001), no. 3, 579622 (electronic); MR1824988 (2002f:22033)], J.-K. Yu has
given a general construction of "tame" supercuspidal representations of G. Yu's construction is
based on the notion of a generic G-datum. There is an irreducible supercuspidal representation
of G associated to every generic G-datum. The paper under review proves that Yu's construction
exhausts all the supercuspidal representations, if G and k satisfy certain hypotheses (which are
met once p is sufficiently large).
Following the methods of Yu's construction, one has a notion of a strongly good positive G-
datum. It is given by a quadruple = (
G, y, -r , - ) satisfying the following conditions: