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arXiv · 2605.12880

Temperley-Lieb Immanants of Ribbon Decomposition Matrices

Son Nguyen·Pavlo Pylyavskyy
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Abstract

Ribbon decomposition matrices give determinantal formulas for skew Schur functions that include as special cases the classical Jacobi-Trudi, Giambelli, and Lascoux-Pragacz formulas. We prove that certain elements of Lusztig's dual canonical basis, called Temperley-Lieb immanants, are Schur-positive when evaluated on ribbon decomposition matrices. We conjecture that this positivity holds for all elements of the dual canonical basis. This is known in the special case of Jacobi-Trudi matrices by a result of Haiman.

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BibTeXRIS

Son Nguyen, Pavlo Pylyavskyy. 2026-09-09. Temperley-Lieb Immanants of Ribbon Decomposition Matrices. https://arxiv.org/abs/2605.12880

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