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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Decomposition of tensor products of irreducible unitary representations


Author: Detlev Poguntke
Journal: Proc. Amer. Math. Soc. 52 (1975), 427-432
MSC: Primary 22D10
DOI: https://doi.org/10.1090/S0002-9939-1975-0384992-0
MathSciNet review: 0384992
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Abstract: It is shown that the tensor product of an irreducible unitary representation of a (discrete) group $ G$ and an $ n$-dimensional $ (n < \infty )$ unitary representation of $ G$ decomposes into at most $ {n^2}$ irreducible subrepresentations; the multiplicity of each irreducible constituent is not greater than $ n$. As an application it is shown that the restriction of an irreducible unitary representation to a subgroup of finite index is a finite sum of irreducible subrepresentations.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0384992-0
Keywords: Irreducible unitary representations of groups, tensor products of representations, intertwining operators
Article copyright: © Copyright 1975 American Mathematical Society