On some Hecke algebra modules arising from theta correspondence and its deformation

Abstract: This talk is based on the joint work with Jiajun Ma and Congling Qiu on theta correspondence of type I dual pairs over a finite field $F_q$. We study the Hecke algebra modules arising from theta correspondence between certain Harish-Chandra series for these dual pairs. We first show that the normalization of the corresponding Hecke algebra is related to the first occurrence index, which leads to proof of the conservation relation. We then study the deformation of this Hecke algebra module at $q=1$ and generalize the results of Aubert-Michel-Rouquier and Pan on theta correspondence between unipotent representations along this way.

number theory

Audience: researchers in the topic

University of Arizona Algebra and Number Theory Seminar