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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A reciprocity theorem for tensor products of group representations


Authors: Calvin C. Moore and Joe Repka
Journal: Proc. Amer. Math. Soc. 64 (1977), 361-364
MSC: Primary 22D12; Secondary 43A65
MathSciNet review: 0450455
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Abstract: Let G be a type I separable locally compact group. By studying a representation of $ G \times G \times G$ we show that a measure class $ \lambda $ on $ G \times G \times G$ which describes the decompositions of tensor products is invariant under permutations, and that the multiplicity $ n({\pi _1},{\pi _2},{\pi _3})$ of $ {\bar \pi _3}$ in $ {\pi _1} \otimes {\pi _2}$ is a symmetric function of its variables up to a $ \lambda $ null set.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0450455-9
PII: S 0002-9939(1977)0450455-9
Article copyright: © Copyright 1977 American Mathematical Society