On products of sln characters and support containment

Let lambda, mu, nu and rho be dominant weights of Sl(n) satisfying lambda+ mu = nu + rho. Let V-lambda denote the highest weight module corresponding to lambda. Lam, Postnikov, Pylyavskyy conjectured a sufficient condition for V-lambda circle times V-mu to be contained in V-nu circle times V-rho as Sl(n)-modules. In this note we prove a weaker version of the conjecture. Namely we prove that under the conjectured conditions every irreducible Sl(n)-module which appears in the decomposition of V-lambda circle times V-mu does appear in the decomposition of V-nu circle times V-rho. (c) 2006 Elsevier Inc. All rights reserved.