Harish-Chandra modules and quantizations

Abstract: Let G be a complex semisimple algebraic group, g its Lie algebra and K a symmetric subgroup of G. In this situation one can talk about Harish-Chandra (g,K)-modules. Their study is a classical chapter of Lie representation theory, largely motivated by the study of representations of semisimple real groups and, in particular, the classification of unitary representations. It is classically expected that Harish-Chandra modules arising from the latter are related to quantizations of nilpotent orbits and their covers. In the recent years, there has been a lot of progress understanding the latter that in particular shed some light on the geometric classification of certain classes of Harish-Chandra modules that should come from unitary representations. I will survey some of this progress in my talk. Based on the joint work with Mason-Brown and Matvieievskyi, arXiv:2108.03453 .

algebraic geometrysymplectic geometry

Audience: researchers in the topic

M-seminar