Events

6.16

16:00-17:00

Event Details:

Title:Lecture by Jiajun Ma:Generic Hecke algebra modules and theta correspondence over finite fields

Venue: Lecture Hall


SpeakerJiajun Ma (Xiamen University Malaysia)



Abstract. In this talk, we consider the theta correspondence of type I dual pairs over a finite field F_q. 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. The conjecture was recently proved by Shu-Yen Pan. These works are based on Srinivasan's formula for the uniform projection of the Weil representation.

 

We will present an alternative approach to the problem using Hecke algebra bimodules. The normalization of the Hecke algebra provides yet another proof of the conservation relation. The specialization of the Hecke bimodule at q=1 recovers the results of AMR and Pan. This work is joint with Congling Qiu and Jialang Zou. If time permits, we will also discuss the relationship between Springer correspondence and theta correspondence based on a geometrization of the above theorem (joint work with Qiu, Yun, and Zou).



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Lecture Seminar