MIT Lie Groups Seminar
Wednesday, May 05, 2021 at 4:30pmVirtual Event
Title: 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
3. the description of the Howe correspondence on unipotent characters in
terms of the symbols by Lusztig.