Knot polynomial identities and quantum group coincidences
Knot polynomial identities and quantum group coincidences
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结多项式恒等式和量子群重合
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
Noah Snyder
中科院分区：
文献类型：
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作者：
S. Morrison;E. Peters;Noah Snyder
我们利用$D_(2n)$次因式平面代数构造了链接不变量，并利用这些不变量证明了有色Jones多项式的某些特化与其他量子纽带多项式的特化之间的关系。这些恒等式也可以通过涉及$D_{2n}$平面代数的偶数部分的小模范类之间的重合来解释。我们讨论了这些重合的起源，解释了$so$水平-秩对偶性、Kirby-Melvin对称性和小动态图的性质。其中一个巧合涉及$G_2$，似乎与水平-秩对偶性无关。
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.
Temperley-Lieb 代数的 Tutte 色恒等式
影响因子：
2
作者：
Fendley P
通讯作者：
Fendley P