纽结多项式恒等式与量子群重合
Knot polynomial identities and quantum group coincidences
摘要：
我们使用$D_{2n}$子因子平面代数构造链接不变量，并使用这些证明新的身份有关的某些专业化的有色琼斯多项式的专业化的其他量子结多项式。这些恒等式也可以用包含$D_{2n}$平面代数偶数部分的小模范畴之间的重合来解释。我们讨论这些巧合的起源，解释的作用，$SO$水平秩的对偶性，柯比-梅尔文对称性，和小Dynkin图的属性。其中一个巧合涉及到$G_2$，似乎与能级-秩对偶无关。
英文摘要：
We construct link invariants using the $D_{2n}$ subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also be explained by coincidences between small modular categories involving the even parts of the $D_{2n}$ planar algebras. We discuss the origins of these coincidences, explaining the role of $SO$ level-rank duality, Kirby-Melvin symmetry, and properties of small Dynkin diagrams. One of these coincidences involves $G_2$ and does not appear to be related to level-rank duality.
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