Structure of Harish-Chandra cells

Abstract: One of the fundamental contributions of Kazhdan and Lusztig's 1979 Inventiones paper was the notion of "cells" in Weyl groups. They gave a decomposition of the left regular representation of W as a direct sum of "left cell" representations, which encode deep and powerful information about group representations. In the case of the symmetric group S_n=W, the left cells are irreducible representations. In all other cases they are not. Lusztig in his 1984 book gave a beautiful description of all left cells in terms of the geometry of a nilpotent orbit. \\ There is a parallel notion of "Harish-Chandra cells" in the representation theory of a real reductive group G(R). Again each cell is a representation of W, encoding deep information about the G(R) representations. I will formulate a conjecture extending Lusztig's calculation of left cell representations to this case, and explain its connection with Arthur's theory of unipotent representations.

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.