地点: 东7报告厅

报告人:马家骏 (厦门大学马来西亚分校)

摘要: 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).

简介：马家骏，于2013年2月在新加坡国立大学取得博士学位。2013年到2016年分别在新加坡国立大学、以色列本古里安大学、香港中文大学等地从事博士后研究工作。随后于2017年1月-2021年6月任职于上海交通大学。于2021年7月入职厦门大学和厦门大学马来西亚分校。长期从事典型群表示论及相关Langlands纲领问题的研究。