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Symmetric pairs with finite-multiplicity property for branching laws of admissible representations. (English) Zbl 1304.22012

This is a survey paper on the complete classification of real reductive symmetric pairs with finite multiplicity property (and bounded multiplicity property), by the author and his collaborators. The proofs of the results of the paper occur in [T. Kobayashi, “Shintani functions, real spherical manifolds, and symmetry breaking operators”, arXiv:1401.0117; T. Kobayashi and T. Matsuki, Transform. Groups 19, No. 2, 457–493 (2014; Zbl 1298.22015); T. Kobayashi and T. Oshima, Adv. Math. 248, 921–944 (2013; Zbl 1317.22010)].

MSC:

22E46 Semisimple Lie groups and their representations
14M15 Grassmannians, Schubert varieties, flag manifolds
53C35 Differential geometry of symmetric spaces
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References:

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