Journal of Lie Theory

no. 4
Reducibility of Generic Unipotent Standard Modules
Dan Barbasch1; Dan Ciubotaru2
1Dept. of Mathematics, Cornell University, Ithaca, NY 14850, U.S.A.
2Dept. of Mathematics, University of Utah, Salt Lake City, UT 84112, U.S.A.
Journal of Lie Theory, Volume 21 (2011) no. 4, pp. 837-846
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.
DOI: 10.5802/jolt.651
Classification: 22E50
Keywords: Whittaker models, unipotent representations, graded affine Hecke algebra

Dan Barbasch  1 ; Dan Ciubotaru  2

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, Volume 21 (2011) no. 4, pp. 837-846. doi: 10.5802/jolt.651
@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},
     doi = {10.5802/jolt.651},
     zbl = {1232.22007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.651/}
}
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  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.651/
DO  - 10.5802/jolt.651
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 https://jolt.centre-mersenne.org/articles/10.5802/jolt.651/
%R 10.5802/jolt.651
%F JOLT_2011_21_4_a4

Cited by Sources: