Kavli Affiliate: Toshiyuki Kobayashi
| First 5 Authors: Toshiyuki Kobayashi, , , ,
| Summary:
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 {it{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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