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.

representation theory

Audience: researchers in the topic

MIT Lie groups seminar

Series comments: Description: Research seminar on Lie groups

This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.