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Abstract : 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.
Document type :
Preprints, Working Papers, ...

https://hal.archives-ouvertes.fr/hal-03664620
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Submitted on : Wednesday, May 11, 2022 - 10:36:22 AM
Last modification on : Thursday, May 12, 2022 - 3:45:54 AM

### Citation

Nicolas Crampé, Luc Vinet, Meri Zaimi. Chern-Simons theory, link invariants and the Askey-Wilson algebra. 2022. ⟨hal-03664620⟩

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