The Newton polytope of the Kronecker product

2023/11/17 by Greta Panova, Chenchen Zhao, Panova, Greta +1 · 2 citations
Mathematics · #05E10 #20C30 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2311.10276

openalex publication_date 2023/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Kronecker product of two Schur functions s_λ∗ 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.

Cited by

• Saturation for Non-Symmetric Macdonald Polynomials
• Supersymmetric Schur polynomials have saturated Newton polytopes

Related

• The Kronecker product of Schur functions indexed by two-row shapes or hook shapes
• The stability of the Kronecker products of Schur functions
• Supersymmetric Schur polynomials have saturated Newton polytopes
• Kronecker products, characters, partitions, and the tensor square conjectures
• Stability of coefficients in the Kronecker product of a hook and a rectangle