University of Sydney Algebra Seminar

Anna Romanov

Friday 29 May, 12-1pm, in Carslaw 175

Lusztig-Vogan categories and a categorial approach to real reductive groups

Soergel bimodules were introduced to tackle hard questions about the representation theory of complex semisimple Lie algebras. Similar (but harder) questions also exist about the representation theory of real reductive Lie groups. Can a Soergel-esque approach be taken in this world? I’ve been thinking about this question for many years. In this talk, I’ll tell you about my perspective on this question. More specifically, I’ll introduce a collection of module categories over Soergel bimodules which encode information about the admissible representation theory of a real reductive group, with a focus on examples.