论文标题
tug-the-hook对称性量子6J符号
Tug-the-hook symmetry for quantum 6j-symbols
论文作者
论文摘要
我们引入了一种新颖的对称性，用于量子6J符号，我们称之为拖网钩对称性。与其他已知的对称性不同，它适用于任何表示形式，包括具有多重性的表示形式。我们提供了一些有利于拖船对称性的证据。首先，这种对称是从特征值猜想的。其次，通过几个具有多重性的6J符号的显式重合的新示例显示了这一点。第三，在3D Chern-Simons理论中，Wilson Loops的拖线钩子对称性意味着量子6J符号的牵引钩对称性。分析的一个重要含义是Chern-Simons Wilson Loops to to links的拖网钩对称性的概括。
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.
