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Structure of the tensor product semigroup

Michael Kapovich·John J. Millson
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Abstract

We study structure of the semigroup Tens(G) consisting of triples of dominant weights (λ,μ,ν) of a complex reductive Lie group G such that the triple tensor product of the corresponding irreducible representations of G has a nonzero G-invariant vector. We prove two general structural results for Tens(G) and give an explicit computation of Tens(G) for G=Sp(4,C) and G=G_2.

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Michael Kapovich, John J. Millson. 2005-08-10. Structure of the tensor product semigroup. https://arxiv.org/abs/math/0508186

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