Knot polynomial identities and quantum group coincidences
نویسندگان
چکیده
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 small Dynkin diagrams. One of these coincidences involves G2 and does not appear to be related to level-rank duality. AMS Classification 18D10 ; 57M27 17B10 81R05 57R56
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تاریخ انتشار 2010