Generic Hecke algebra modules in theta correspondence over finite fields

Time：Mon., 10:00-11:30am, Sept.4, 2023

Venue：Jingzhai 静斋 304

Organizer：Will Donovan, Penghui Li Peng Shan, Changjian Su

Speaker：Jiajun Ma 马家骏 Xiamen University

Abstract

In this talk, we consider the theta correspondence of type I dual pairs over a finite. Aubert, Michel, and Rouquier established an explicit formula for theta correspondence between unipotent representations of unitary groups and made a conjecture for the symplectic group-even orthogonal group dual pair. Shu-Yen Pan recently proved the conjecture. These works are based on Srinivasan's formula for the uniform projection of the Weil representation.

Joint with Congling Qiu and Jialang Zou, we found an alternative approach to solve the problem by analyzing the relevant Hecke algebra bimodules. Joint with Zhiwei Yun, we geometrized the whole picture. Consequently, we obtained a relation between the Springer correspondence and theta correspondence.

About the speaker

Jiajun Ma is an Associate Professor at Xiamen University. His research interests are Theta Correspondence, Representation Theory of reductive groups, Invariant Theory.

Personal Homepage：

https://www.majiajun.org/

DATESeptember 4, 2023

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