Tug-the-hook symmetry for quantum 6j-symbols
Abstract
We introduce a novel symmetry for quantum 6j-symbols, which we call the tug-the-hook symmetry. Unlike other known symmetries, it is applicable for any representations, including ones with multiplicities. We provide several evidences in favour of the tug-the-hook symmetry. First, this symmetry follows from the eigenvalue conjecture. Second, it is shown by several new examples of explicit coincidence of 6j-symbols with multiplicities. Third, the tug-the-hook symmetry for Wilson loops for knots in the 3d Chern-Simons theory implies the tug-the-hook symmetry for quantum 6j-symbols. An important implication of the analysis is the generalization of the tug-the-hook symmetry for the Chern-Simons Wilson loops to the case of links.
Keywords
Cite
@article{arxiv.2210.07874,
title = {Tug-the-hook symmetry for quantum 6j-symbols},
author = {E. Lanina and A. Sleptsov},
journal= {arXiv preprint arXiv:2210.07874},
year = {2023}
}
Comments
12 pages, published version