On products of sln characters and support containment

Galyna Dobrovolska; Pavlo Pylyavskyy

doi:10.1016/j.jalgebra.2006.10.033

On products of sl_n characters and support containment

Galyna Dobrovolska
, Pavlo Pylyavskyy

School of Mathematics

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

Let λ, μ, ν and ρ be dominant weights of 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 ⊗ V_μ to be contained in V_ν ⊗ V_ρ 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_λ ⊗ V_μ does appear in the decomposition of V_ν ⊗ V_ρ.

Original language	English (US)
Pages (from-to)	706-714
Number of pages	9
Journal	Journal of Algebra
Volume	316
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2006.10.033
State	Published - Oct 15 2007

Bibliographical note

Funding Information:
✩ The research was funded by SPUR program at MIT. * Corresponding author. E-mail addresses: [email protected] (G. Dobrovolska), [email protected], [email protected] (P. Pylyavskyy).

Keywords

Horn-Klyachko inequalities
Schur functions

Publisher link

10.1016/j.jalgebra.2006.10.033

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Cite this

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title = "On products of sln characters and support containment",

abstract = "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.",

keywords = "Horn-Klyachko inequalities, Schur functions",

author = "Galyna Dobrovolska and Pavlo Pylyavskyy",

note = "Funding Information: ✩ The research was funded by SPUR program at MIT. * Corresponding author. E-mail addresses: [email protected] (G. Dobrovolska), [email protected], [email protected] (P. Pylyavskyy).",

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AU - Pylyavskyy, Pavlo

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N2 - 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.

AB - 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.

KW - Horn-Klyachko inequalities

KW - Schur functions

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