On a convexity property of tensor products of irreducible, rational representations of $SL(n)$

Abstract

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 $SL(n)$ 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 $SL(n)$.

6 pages, example added to indicate failure of convexity property for B_n type Lie algebras; to appear in Journal of Lie Theory