Odd knot invariants from quantum covering groups

Clark, Sean

doi:10.2140/agt.2017.17.2961

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Odd knot invariants from quantum covering groups

Sean Clark

Algebraic & Geometric Topology 17 (2017) 2961–3005

DOI: 10.2140/agt.2017.17.2961

Abstract

We show that the quantum covering group associated to $o s p (1 | 2 n)$ has an associated colored quantum knot invariant à la Reshetikhin–Turaev, which specializes to a quantum knot invariant for $o s p (1 | 2 n)$ , and to the usual quantum knot invariant for $s o (1 + 2 n)$ . In particular, this furnishes an “odd” variant of $s o (1 + 2 n)$ quantum invariants, even for knots labeled by spin representations. We then show that these knot invariants are essentially the same, up to a change of variables and a constant factor depending on the knot and weight.

Keywords

quantum groups, knot invariants, Lie superalgebra

Mathematical Subject Classification 2010

Primary: 17B37, 57M27

References

Publication

Received: 18 October 2016

Revised: 28 February 2017

Accepted: 9 May 2017

Published: 19 September 2017

Authors

Sean Clark
Department of Mathematics Northeastern University Boston, MA United States
https://web.northeastern.edu/sclark/

Volume 17, issue 5 (2017)