Orbit method: From matrices to unitary representations

Hybrid talk. For zoom details contact Christian Kaiser (kaiser@mpim-bonn.mpg.de)

The talk is intended as a leisurely introduction to one of the fundamental tasks of representation theory: the construction of irreducible unitary representations. I will first discuss some philosophical sources of unitary representations of Lie groups (Kirillov theory and Arthur’s classification).  I will then discuss a recent development (due to Barbasch, Ma, Sun and the speaker) on Vogan’s problem of unipotent representations, which is to associate irreducible unitary representations to nilpotent matrices (which behave like zero but are not zero). We solve the mystery for those nilpotent matrices which are special in the sense of Lusztig.