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The restriction of an irreducible unitary representation π of a real reductive group G to a reductive subgroup H decomposes into a direct integral of irreducible unitary representations τ of H with multiplicities m(π,τ) ∈ N ∪ {∞}. We show that on the smooth vectors of π, the direct integral is pointwise defined. This implies that m(π,τ) is bounded above by the dimension of the space Hom H(π ∞| H,τ ∞) of intertwining operators between the smooth vectors, also called symmetry breaking operators, and provides a precise relation between these two concepts of multiplicity.
Original language | English |
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Journal | Journal of Lie Theory |
Volume | 32 |
Issue | 1 |
Pages (from-to) | 191-196 |
Number of pages | 5 |
ISSN | 0949-5932 |
Publication status | Published - 2022 |
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ID: 205547651