Harish-Chandra's admissibility theorem and beyond. Harish-Chandra Centenary Celebrations 2023: Conference on Harish-Chandra. Harish-Chandra Research Institute (HRI) in Allahabad, India, 9-14 October 2023.

Let $G$ be a real reductive linear Lie group, and $K$ a maximal compact subgroup. Harish-Chandra's renowned admissibility theorem asserts that any irreducible unitary representation of $G$ decomposes into a direct sum of irreducible $K$-modules with each multiplicity finite. In this talk, we discuss to which extent such nice properties hold for a more general setting when we restrict representations to non-compact subgroups $G'$. If time permits, I would like to mention its application to another apparently very different problem, that is, spectral analysis on locally semisimple symmetric spaces.
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© Toshiyuki Kobayashi