CLASSIFICATION OF FINITE-MULTIPLICITY SYMMETRIC PAIRS

By Toshiyuki Kobayashi, T. Matsuki. 2013

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We give a complete classification of the reductive symmetric pairs (G, H) for which the homogeneous space (G × H)/ diag H is real spherical in the sense that a minimal parabolic subgroup has an open orbit. Combining with a criterion established in T. Kobayashi, T. Oshima, Adv. Math. 2013, we give a necessary and sufficient condition for a reductive symmetric pair (G, H) such that the multiplicities for the branching law of the restriction of any admissible smooth representation of G to H have finiteness/boundedness property.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bee22c08443ddf45eb968112cf866355708c081e