Abstract
Let ρ be half the sum of the positive roots of a root system. We prove that if ⋋ is a dominant weight, ⋋ ≤ 2ρ with respect to the dominance order, and d is a saturation factor for the complex Lie algebra associated to the root system, then the irreducible representation V (d⋋) appears in the tensor product V (dρ) ⊗ V (dρ).
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