Generic Hecke algebra and theta correspondence over finite fields

Jia-Jun Ma, Congling Qiu, Jialiang Zou

Published 2022-07-31Version 1

We study the Hecke modules arising from theta correspondence for type (I) dual pairs over finite fields. For the product of the pair of generic Hecke algebras under consideration, we show that there is a generic Hecke module whose specializations at prime powers give all the Hecke modules. As an application, we generalize the results of Aubert-Michel-Rouquier and Pan on theta correspondence between Harish-Chandra series.