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Journal of Lie Theory 32 (2022), No. 1, 023--028
Copyright Heldermann Verlag 2022

On a Convexity Property of Tensor Products of Irreducible, Rational Representations of SL(n)

Hariharan Narayanan
School of Technology and Computer Science, Tata Institute of Fundamental Research, Mumbai, India

Conjeeveram S. Rajan
School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India

The aim of this note is to point out a convexity property with respect to the root lattice for the support of the highest weights that occur in a tensor product of irreducible rational representations of SL(n) (or more generally any Lie group over which the saturation property holds) over the complex numbers. The observation is a consequence of the convexity properties of the saturation cone and the validity of the saturation conjecture for SL(n).

Keywords: Tensor products, SL(n), convexity.

MSC: 20G05; 22E45, 05E10.

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