论文标题
Chern-Simons理论，链接不变性和Askey-Wilson代数
Chern-Simons theory, link invariants and the Askey-Wilson algebra
论文作者
论文摘要
$ su（2）$ chern-simons（cs）理论和reshetikhin-turaev（rt）链接不变结构中的Askey-Wilson（AW）代数的出现在带有量子代数$ u_q（\ Mathfrak {sufrak {su} _2）$中。带有三个线的缠结图与旋转$ 1/2 $封闭环相连与AW代数的发电机相关联。在CS理论和RT结构中都表明，这些缠结的链接不变遵守AW发生器的关系。因此，在CS理论中，某些Wilson循环的期望值满足AW代数决定的关系，并且链接不变式没有区分链接的相应线性组合。
The occurrence of the Askey-Wilson (AW) algebra in the $SU(2)$ Chern-Simons (CS) theory and in the Reshetikhin-Turaev (RT) link invariant construction with quantum algebra $U_q(\mathfrak{su}_2)$ is explored. Tangle diagrams with three strands with some of them enclosed in a spin-$1/2$ closed loop are associated to the generators of the AW algebra. It is shown in both the CS theory and RT construction that the link invariant of these tangles obey the relations of the AW generators. It follows that the expectation values of certain Wilson loops in the CS theory satisfy relations dictated by the AW algebra and that the link invariants do not distinguish the corresponding linear combinations of links.
