Dragan Milicic (University of Utah) is speaking in the Algebra Seminar this week. We will go out for lunch after the talk. When: Friday, 15 September, 12-1pm Where: Carslaw 173 Title: On orthogonality relations Abstract: Schur orthogonality relations are one of the basic results of representation theory of finite groups. Hermann Weyl used their extension to compact groups to determine irreducible characters of compact Lie groups. Later, Harish-Chandra generalized them to discrete series of noncompact reductive Lie groups. At that time, they looked like a clever computational trick to determine the characters of discrete series. In this talk, we are going to discuss a categorical generalization of the orthogonality relations to arbitrary admissible representations of reductive Lie groups. It contains all other situations as special cases.