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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.

Dan Ciubotaru
Dept. of Mathematics, University of Utah, Salt Lake City, UT 84112, U.S.A.

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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