T. Kobayashi. Harish-Chandra's admissibility theorem and beyond. preprint. 32 pages.

This article is a record of the lecture at the centennial conference for Harish-Chandra. The admissibility theorem of Harish-Chandra concerns the restrictions of irreducible representations to maximal compact subgroups. In this article, we begin with a brief explanation of two directions for generalizing his pioneering work to non-compact reductive subgroups: one emphasizes discrete decomposability with the finite multiplicity property, while the other focuses on finite/uniformly bounded multiplicity properties. We discuss how the recent representation-theoretic developments in these directions collectively offer a powerful method for the new spectral analysis of standard locally symmetric spaces, extending beyond the classical Riemannian setting.

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© Toshiyuki Kobayashi