What question did this study set out to answer?

This research aims to identify the reducibility points of standard modules for the affine Hecke algebra when the inducing data is generic.

March 29, 2026Open Access

Reducibility of Generic Unipotent Standard Modules

DBD. Barbasch DCD. Ciubotaru

Key Points

This research aims to identify the reducibility points of standard modules for the affine Hecke algebra when the inducing data is generic.
Utilized Lusztig's geometric classification approach.
Analyzed standard modules for the affine Hecke algebra.
Explored known results from previous literature on split p-adic groups.
Identified reducibility points consistent with previous findings by Mui and Shahidi.
Established a necessary, yet insufficient, condition for reducibility in the nongeneric scenario.

Abstract

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 Mui 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 nongeneric case.

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