Journal of Lie Theory 21 (2011), No. 4, 837--846
Copyright Heldermann Verlag 2011
Reducibility of Generic Unipotent Standard Modules
Dan Barbasch
Dept. of Mathematics, Cornell University, Ithaca, NY 14850, U.S.A.
barbasch@math.cornell.edu
Dan Ciubotaru
Dept. of Mathematics, University of Utah, Salt Lake City, UT 84112, U.S.A.
ciubo@math.utah.edu
Using Lusztig's geometric classification, we find the reducibility points of a standard module for the affine Hecke algebra, in the case when the inducing data is generic. This recovers the known result of Muic and Shahidi for representations of split p-adic groups with Iwahori-spherical Whittaker vectors. We also give a necessary (but insufficient) condition for reducibility in the non-generic case.
Keywords: Whittaker models, unipotent representations, graded affine Hecke algebra.
MSC: 22E50
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