Harish-Chandra's admissibility theorem and beyond. Representations and Characters: Revisiting the Works of Harish-Chandra and André Weil — A satellite conference of the virtual ICM 2022 (organized by Hung Yean Loke, Tomasz Przebinda, Angela Pasquale, and Binyong Sun). The Institute for Mathematical Sciences, National University of Singapore, Singapore, 9 July 2022.

Let $G$ be a real reductive linear Lie group, and K a maximal compact subgroup of $G$. Harish-Chandra's admissibility theorem asserts that any irreducible unitary representation decomposes into a direct sum of irreducible $K$-modules with each multiplicity finite. In this talk, we consider a non-compact reductive subgroup $G'$ instead of compact $K$, and discuss the restriction of an irreducible representation of $G$ to the subgroup $G'$ with focus on $G'$-admissible property (i.e. discretely decomposable with finite multiplicity) as well as on uniformly bounded multiplicity property.

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© Toshiyuki Kobayashi