T. Kobayashi. Admissible restrictions of irreducible representations of reductive Lie groups: Symplectic geometry and discretely decomposability. preprint, 20 pages. arXiv: 1907.12964.

Let G be a real reductive Lie group, L a compact subgroup, and π an irreducible admissible representation of G. This paper proves a necessary and sufficient condition for the finiteness of the multiplicities of L-types occurring in π based on symplectic techniques. This leads us to a new proof of the criterion for the discrete decomposability of the restriction of unitary representations with respect to noncompact subgroups (the author, Ann. Math. 1998). A number of examples are presented in connection with Kostant's convexity theorem and also with non-Riemannian locally symmetric spaces.

arXiv | preprint version(pdf) ]

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