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arXiv · 2109.11378

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

Álvaro Gutiérrez·Mercedes H. Rosas
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Abstract

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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Álvaro Gutiérrez, Mercedes H. Rosas. 2023-05-30. Necessary conditions for the positivity of Littlewood-Richardson and plethystic coefficients. https://doi.org/10.5802/crmath.468

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