Journal article
Tangle functors from semicyclic representations
Journal of knot theory and its ramifications, Vol.26(11), p.1750065
10/01/2017
DOI: 10.1142/S0218216517500651
Abstract
Let q be a 2Nth root of unity where N is odd. Let U-q(epsilon) (sl(2)) denote the quantum group with large center corresponding to the Lie algebra sl(2)C with generators E, F, K, and K-1. A semicyclic representation of U-q(epsilon) (sl(2)) is an N-dimensional irreducible representation rho : U-q(s) (sl(2)) -> MN(C), so that rho(E-N) = aId with a not equal 0, rho(F-N) = 0 and rho(K-N) = Id. We construct a tangle functor for framed homogeneous tangles colored with semicyclic representations, and prove that for (1, 1)-tangles coming from knots, the invariant defined by the tangle functor coincides with Kashaev's invariant.
Details
- Title: Subtitle
- Tangle functors from semicyclic representations
- Creators
- Nathan Druivenga - University of KentuckyCharles Frohman - University of IowaSanjay Kumar - Michigan State University
- Resource Type
- Journal article
- Publication Details
- Journal of knot theory and its ramifications, Vol.26(11), p.1750065
- DOI
- 10.1142/S0218216517500651
- ISSN
- 0218-2165
- eISSN
- 1793-6527
- Publisher
- WORLD SCIENTIFIC PUBL CO PTE LTD
- Number of pages
- 21
- Language
- English
- Date published
- 10/01/2017
- Academic Unit
- Mathematics
- Record Identifier
- 9984241152702771
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