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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}(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 

Journal  Journal of Lie Theory 
Volume  32 
Issue  1 
Pages (fromto)  191196 
Number of pages  5 
ISSN  09495932 
Publication status  Published  2022 
Keywords
 Real reductive groups
 branching laws
 direct integral
 pointwise defined
 smooth vectors
 symmetry breaking operators
 unitary representations
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Dive into the research topics of 'On the direct integral decomposition in branching laws for real reductive groups'. Together they form a unique fingerprint.Projects
 1 Finished

Symmetry Breaking in Mathematics
Frahm, J. (PI), Weiske, C. (Participant), Ditlevsen, J. (Participant), Spilioti, P. (Participant), BangJensen, F. J. (Participant) & Labriet, Q. (Participant)
01/08/2019 → 31/07/2024
Project: Research