论文标题
反平行三重椒盐脆饼的差异膨胀：分解变形的方式
Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed
论文作者
论文摘要
对于一个奇特的双辫子结家族，有一个显着的分解公式，用于差分（环形）膨胀（DE）的系数，如今，该系数被广泛用于构建独家的RACAH矩阵$ s $ s $和$ \ bar s $在任意表示中。分解的起源仍然晦涩难懂，双辫子的特殊作用仍然是一个谜。为了拓宽视角，我们将双辫子的家族延伸到反平行三重椒盐脆饼，这些椒盐脆饼是通过从Trefoil的呈现不足的变形而获得的，并且所有这些变形都具有零缺陷。事实证明，DE系数的分解非常严重，至少对于所有对称表示，仍然由优雅的公式描述。
For a peculiar family of double braid knots there is a remarkable factorization formula for the coefficients of the differential (cyclotomic) expansion (DE), which nowadays is widely used to construct the exclusive Racah matrices $S$ and $\bar S$ in arbitrary representations. The origins of the factorization remain obscure and the special role of double braids remains a mystery. In an attempt to broaden the perspective, we extend the family of double braids to antiparallel triple pretzels, which are obtained by the defect-preserving deformation from the trefoil and all have defect zero. It turns out that factorization of DE coefficients is violated quite strongly, still remains described by an elegant formula, at least for all symmetric representations.
