Knot polynomial identities and quantum group coincidences
We construct link invariants using the D2n 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 D2n planar algebras. We discuss the origins of these coincidences, explaining the role of SO level-rank duality, Kirby�Melvin symmetry, and properties of...[Show more]
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