The Newton polytope of the Kronecker product
Abstract
We study the Kronecker product of two Schur functions sλ sμ, defined as the image of the characteristic map of the product of two Sn 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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