On products of sl_n characters and support containment

2006/08/04 by Galyna Dobrovolska, Dobrovolska, Galyna, Pavlo Pylyavskyy +1 · 2 citations
Mathematics · #05E05 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT) #math.CO #math.RT #msc:05E05

paper · pdf · doi:10.48550/arxiv.math/0608134

9 pages, 5 figures

arxiv created 2006/08/04 · openalex publication_date 2006/08/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let λ, μ, ν and ρ be dominant weights of \mathfraksl_n satisfying λ+ μ= ν+ ρ. Let V_λ denote the highest weight module corresponding to λ. Lam, Postnikov, Pylyavskyy conjectured a sufficient condition for V_λ ⊗ V_μ to be contained in V_ν ⊗ V_ρ as \mathfraksl_n-modules. In this note we prove a weaker version of the conjecture. Namely we prove that under the conjectured conditions every irreducible \mathfraksl_n-module which appears in the decomposition of V_λ ⊗ V_μ does appear in the decomposition of V_ν ⊗ V_ρ.

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