MIT Lie Groups Seminar

Speaker: Jialiang Zou (U. of Michigan)

Title: On some Hecke algebra modules arising from theta correspondence and it’s 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 a  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