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Multiplicities in the Tensor Product of Finite-Dimensional Representations of Discrete Groups
Published online by Cambridge University Press: 20 November 2018
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Let G be a group and ρ and σ two irreducible unitary representations of G in complex Hilbert spaces and assume that dimp ρ= n < ∞. D. Poguntke [2] proved that 
is a sum of at most n2 irreducible subrepresentations. The case when dim a is also finite he attributed to R. Howe.
We shall prove analogous results for arbitrary finite-dimensional representations, not necessarily unitary. Thus let F be an algebraically closed field of characteristic 0. We shall use the language of modules and we postulate that allour modules are finite-dimensional as F-vector spaces. The field F itself will be considered as a trivial G-module.
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- Copyright © Canadian Mathematical Society 1978
References
1.
Hochschild, G.: Introduction to affine algebraic groups, Holden-Day, San Francisco 1971.Google Scholar
2.
Poguntke, D.: Decomposition of tensor products of irreducible unitary representations, Proc. Amer. Math-Soc. 52 (1975), 427-432.Google Scholar
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