Classification of finite-multiplicity symmetric pairs

Abstract

We give a complete classification of the reductive symmetric pairs (G,H) for which the homogeneous space $(G\times H)/diag(H)$ 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 any admissible smooth representation of $G$ to $H$ have finiteness/boundedness property.

To appear in Transformation Groups 19 (2014)

References in corpus (5)

• Finite multiplicity theorems for induction and restriction
• Classification of discretely decomposable A_q(λ) with respect to reductive symmetric pairs
• F-method for symmetry breaking operators
• Classification of symmetric pairs with discretely decomposable restrictions of (g,K)-modules
• Generalized Bernstein--Reznikov integrals

Cited by in corpus (13)

• A program for branching problems in the representation theory of real reductive groups
• Shintani functions, real spherical manifolds, and symmetry breaking operators
• Branching laws of unitary representations associated to minimal elliptic orbits for indefinite orthogonal group O(p,q)
• Decomposition Theorems for Triple Spaces
• Classification of reductive real spherical pairs II. The semisimple case
• Annihilator varieties of distinguished modules of reductive Lie algebras
• Symmetry breaking operators for real reductive groups of rank one
• Multiplicity in restricting minimal representations
• Strong Gelfand subgroups of $F\wr S_n$
• Real double flag varieties for the symplectic group
• Recent advances in branching problems of representations
• Topics on global analysis of manifolds and representation theory of reductive groups
• Generating operators of symmetry breaking -- from discrete to continuous