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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.

References [Enhancements On Off] (What's this?)

  • [1] A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57-110 = Russian Math. Surveys 17 (1962), no. 4, 53-104. MR 25 #5396. MR 0142001 (25:5396)
  • [2] G. W. Mackey, Induced representations of locally compact groups, II. The Frobenius reciprocity theorem, Ann. of Math. (2) 58 (1953), 193-221. MR 15, 101. MR 0056611 (15:101a)
  • [3] J. Repka, Tensor products of unitary representations of $ \mathrm{SL}_2(R)$, Bull. Amer. Math. Soc. 82 (1976), 930-932. MR 0425026 (54:12984)

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