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University of Sydney Algebra Seminar

Dragan Milicic

Friday 15 September, 12-1pm, Place: Carslaw 173

On orthogonality relations

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.