Finite Howe correspondence and Lusztig classification

Abstract: Let $(G,G')$ be a reductive dual pair inside a finite symplectic group. By restricting the Weil representation to the dual pair, there exists a relation (called the finite Howe correspondence) between the irreducible representations of the two groups $G,G'$. In this talk, we would like to discuss some progress on the understanding of the correspondence by using Lusztig's classification on the representations of finite classical groups.

In particular, we will focus on the following three subjects: 1. the decomposition of the uniform projection of the Weil character 2. the commutativity between the Howe correspondence and the Lusztig correspondence 3. the description of the Howe correspondence on unipotent characters in terms of the symbols by Lusztig.

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.