Quantum $\mathfrak{sl}(n,\mathbb{C})$ link invariants

Details Quantum $\mathfrak{sl}(n,\mathbb{C})$ link invariants Quantum $\mathfrak{sl}(n,\mathbb{C})$ link invariants

2005-06-20

arxiv.org/abs/math/0506403v3

Mathematics

Geometric Topology

19 pages, 18 figures

Scientific paper

In this paper, we study the quantum sl(n) representation category using the web space. Specially, we extend sl(n) web space for $n\ge 4$ as generalized Temperley-Lieb algebras. As an application of our study, we find that the HOMFLY polynomial P_n(q) specialized to a one variable polynomial can be computed by a linear expansion with respect to a presentation of the quantum representation category of sl(n). Moreover, we correct the false conjecture \cite{PS:superiod} given by Chbili, which addresses the relation between some link polynomials of a periodic link and its factor link such as Alexander polynomial (n = 0) and Jones polynomial (n = 2) and prove the corrected conjecture not only for HOMFLY polynomial but also for the colored HOMFLY polynomial specialized to a one variable polynomial.

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