Let λ, μ, ν and ρ be dominant weights of sln satisfying λ + μ = ν + ρ. Let Vλ denote the highest weight module corresponding to λ. Lam, Postnikov, Pylyavskyy conjectured a sufficient condition for Vλ ⊗ Vμ to be contained in Vν ⊗ Vρ as sln-modules. In this note we prove a weaker version of the conjecture. Namely we prove that under the conjectured conditions every irreducible sln-module which appears in the decomposition of Vλ ⊗ Vμ does appear in the decomposition of Vν ⊗ Vρ.
Bibliographical noteFunding Information:
✩ The research was funded by SPUR program at MIT. * Corresponding author. E-mail addresses: email@example.com (G. Dobrovolska), firstname.lastname@example.org, email@example.com (P. Pylyavskyy).
- Horn-Klyachko inequalities
- Schur functions