Temperley-Lieb Immanants of Ribbon Decomposition Matrices
Combinatorics
2026-05-19 v2 Representation Theory
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.
Cite
@article{arxiv.2605.12880,
title = {Temperley-Lieb Immanants of Ribbon Decomposition Matrices},
author = {Son Nguyen and Pavlo Pylyavskyy},
journal= {arXiv preprint arXiv:2605.12880},
year = {2026}
}
Comments
Fix citations and acknowledgement