Littlewood-Richardson系数和plethystic系数正的必要条件

Pub Date : 2023-10-24 DOI:10.5802/crmath.468

Álvaro Gutiérrez, Mercedes H. Rosas

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引用次数: 1

摘要

给出了Littlewood-Richardson系数和SXP系数正的必要条件。我们推导出多倍体系数为正的必要条件。明确地，我们的主要结果表明，如果S λ (V)在S μ (S ν (V))的不可约分解中以求和形式出现，则ν的图包含在λ的图中。

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Necessary conditions for the positivity of Littlewood–Richardson and plethystic coefficients

We give necessary conditions for the positivity of Littlewood–Richardson coefficients and SXP coefficients. We deduce necessary conditions for the positivity of the plethystic coefficients. Explicitly, our main result states that if S λ (V) appears as a summand in the decomposition into irreducibles of S μ (S ν (V)), then ν’s diagram is contained in λ’s diagram.

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