On the direct integral decomposition in branching laws for real reductive groups

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Abstract

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| H) of intertwining operators between the smooth vectors, also called symmetry breaking operators, and provides a precise relation between these two concepts of multiplicity.

OriginalsprogEngelsk
TidsskriftJournal of Lie Theory
Vol/bind32
Nummer1
Sider (fra-til)191-196
Antal sider5
ISSN0949-5932
StatusUdgivet - 2022

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  • Symmetry Breaking in Mathematics

    Frahm, J. (PI), Weiske, C. (Deltager), Ditlevsen, J. (Deltager), Spilioti, P. (Deltager), Bang-Jensen, F. J. (Deltager) & Labriet, Q. (Deltager)

    01/08/201931/07/2024

    Projekter: ProjektForskning

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