On tensor products of polynomial representations

Abstract

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.

9 pages; final version to appear in Canad. Math. Bull

Cited by in corpus (2)

• Posets, Tensor Products and Schur positivity
• On the uniqueness of promotion operators on tensor products of type A crystals