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.
1
Dept. of Mathematics, Cornell University, Ithaca, NY 14850, U.S.A.
2
Dept. of Mathematics, University of Utah, Salt Lake City, UT 84112, U.S.A.
Dan Barbasch; Dan Ciubotaru. Reducibility of Generic Unipotent Standard Modules. Journal of Lie Theory, Tome 21 (2011) no. 4, pp. 837-846. http://geodesic.mathdoc.fr/item/JOLT_2011_21_4_a4/
@article{JOLT_2011_21_4_a4,
author = {Dan Barbasch and Dan Ciubotaru},
title = {Reducibility of {Generic} {Unipotent} {Standard} {Modules}},
journal = {Journal of Lie Theory},
pages = {837--846},
year = {2011},
volume = {21},
number = {4},
url = {http://geodesic.mathdoc.fr/item/JOLT_2011_21_4_a4/}
}
TY - JOUR
AU - Dan Barbasch
AU - Dan Ciubotaru
TI - Reducibility of Generic Unipotent Standard Modules
JO - Journal of Lie Theory
PY - 2011
SP - 837
EP - 846
VL - 21
IS - 4
UR - http://geodesic.mathdoc.fr/item/JOLT_2011_21_4_a4/
ID - JOLT_2011_21_4_a4
ER -
%0 Journal Article
%A Dan Barbasch
%A Dan Ciubotaru
%T Reducibility of Generic Unipotent Standard Modules
%J Journal of Lie Theory
%D 2011
%P 837-846
%V 21
%N 4
%U http://geodesic.mathdoc.fr/item/JOLT_2011_21_4_a4/
%F JOLT_2011_21_4_a4
