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arXiv · 2511.08969

Hadamard Products of dual Jacobi-Trudi matrices

Robert Angarone·Jang Soo Kim·Jaeseong Oh·Daniel Soskin
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Abstract

We study positivity properties of Hadamard products of Jacobi-Trudi matrices. Mal\'{o} proved that the Hadamard (entrywise) product of two totally positive upper-triangular Toeplitz matrices whose Toeplitz sequences are the coefficient sequences of real-rooted polynomials with nonpositive zeros is again totally positive. Sokal conjectured that this result can be strengthened to total monomial positivity for the Hadamard product of Jacobi-Trudi matrices. In this paper we show that Temperley-Lieb immanants are Schur positive for Hadamard products of Jacobi-Trudi matrices given by ribbon-like skew shapes. In particular, we affirm Sokal's conjecture for minors given by ribbon-like skew shapes. Moreover, we provide a manifestly positive Schur expansion for Temperley-Lieb immanants evaluated on the Hadamard product of Jacobi-Trudi matrices indexed by ribbons. In addition, for the ribbon case, we construct a corresponding representation, offering a representation-theoretic proof of the Schur positivity.

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Robert Angarone, Jang Soo Kim, Jaeseong Oh, Daniel Soskin. 2025-11-12. Hadamard Products of dual Jacobi-Trudi matrices. https://arxiv.org/abs/2511.08969

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