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arXiv · 2605.10608

Hidden Structure of Jack Littlewood-Richardson Coefficients

Ryan Mickler
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Abstract

We argue that Jack Littlewood-Richardson coefficients $g_{μν}^λ(α)$ are specialisations of certain novel polynomials. For the triple of partitions $(μ,ν,λ)=(21,21,321)$, we prove the corresponding polynomial is invariant under $S_6 \times \mathbb{Z}_2$, which is identified as the automorphism group of the Johnson graph $J(6,3)$. We conjecture that these polynomials exhibit a factorization property on certain hyperplanes, which is a consequence of compatibility relations between polynomials associated to adjacent triples in the Young graph. As a consequence of this, we conjecture that the difference of adjacent Jack Littlewood-Richardson coefficients is divisible by the shared hook length.

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Ryan Mickler. 2026-05-11. Hidden Structure of Jack Littlewood-Richardson Coefficients. https://arxiv.org/abs/2605.10608

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