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arXiv · 2311.10276

The Newton polytope of the Kronecker product

Greta Panova·Chenchen Zhao
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Abstract

We study the Kronecker product of two Schur functions $s_λ\ast s_μ$, defined as the image of the characteristic map of the product of two $S_n$ irreducible characters. We prove special cases of a conjecture of Monical--Tokcan--Yong that its monomial expansion has a saturated Newton polytope. Our proofs employ the Horn inequalities for positivity of Littlewood-Richardson coefficients and imply necessary conditions for the positivity of Kronecker coefficients.

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Greta Panova, Chenchen Zhao. 2025-04-02. The Newton polytope of the Kronecker product. https://arxiv.org/abs/2311.10276

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