Structure of the tensor product semigroup

Details Structure of the tensor product semigroup Structure of the tensor product semigroup

2005-08-10

arxiv.org/abs/math/0508186v1

Mathematics

Representation Theory

46 pages

Scientific paper

We study structure of the semigroup Tens(G) consisting of triples of dominant
weights (\lambda,\mu,\nu) 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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