Applications of Hecke Algebra in the Representation of Reductive Groups

Abstract: Consider a reductive linear algebraic group G. Let H be the generic Hecke algebra attached to the Weyl group of G. The representations of G and H have many deep connections. In this talk, I will discuss our two recent works where Hecke algebras play a crucial role: 1. Counting special unipotent representations of real reductive groups 2. Determining the theta correspondence over finite fields. I will also discuss the analog picture in the theta correspondence over p-adic fields when time permits.

Mathematics

Audience: researchers in the topic

Comments: Hybrid talk

Zoom livestream: ID 743 736 2326 / Password 013049

PKU/BICMR Number Theory Seminar