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
hariharan.narayanan@tifr.res.in
Conjeeveram S. Rajan
School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India
rajan@math.tifr.res.in
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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