On tensor products of polynomial representations

Kevin Purbhoo, Stephanie van Willigenburg

Published 2007-06-22Version 1

We determine the necessary and sufficient combinatorial conditions for which the tensor product of two irreducible polynomial representations of $GL(n,\mathbb{C})$ is isomorphic to another. As a consequence we discover families of Littlewood-Richardson coefficients that are non-zero, and a condition on Schur non-negativity.