Combinatorial Theory

We study the Kronecker product of two Schur functions \(s_\lambda\ast s_\mu\), 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.

Mathematics Subject Classifications: 05E10, 20C30

Keywords: Kronecker coefficients, saturated Newton polytope, symmetric group representations