Séminaire Lotharingien de Combinatoire, 91B.52 (2024), 12 pp.

Greta Panova and Chenchen Zhao

The Newton Polytope of The Kronecker Product

Abstract. We study the Kronecker product of two Schur functions s_λ_*s_μ, whose Schur expansion is given by the Kronecker coefficients g(λ,μ,ν) of the symmetric group. We prove special cases of a conjecture of Monical, Tokcan and 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.

Received: November 15, 2023. Accepted: February 15, 2024. Final version: April 1, 2024.

The following versions are available:

PDF (186 K)
TeX version