On products of sl_n characters and support containment

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Let $λ$, $μ$, $ν$ and $ρ$ be dominant weights of $\mathfrak{sl_n}$ satisfying $λ+ μ= ν+ ρ$. Let $V_λ$ denote the highest weight module corresponding to $λ$. Lam, Postnikov, Pylyavskyy conjectured a sufficient condition for $V_λ \otimes V_μ$ to be contained in $V_ν \otimes V_ρ$ as $\mathfrak{sl_n}$-modules. In this note we prove a weaker version of the conjecture. Namely we prove that under the conjectured conditions every irreducible $\mathfrak{sl_n}$-module which appears in the decomposition of $V_λ \otimes V_μ$ does appear in the decomposition of $V_ν \otimes V_ρ$.
9 pages, 5 figures

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Combinatorics, Representation Theory, 05E05

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http://salesiana.dossiersoluciones.com/handle/123456789/115297

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0608134
 http://arxiv.org/abs/math/0608134

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arXiv