The colored HOMFLY polynomial is q-holonomic
Geometric Topology
2012-11-28 v1 High Energy Physics - Theory
Quantum Algebra
Abstract
We prove that the colored HOMFLY polynomial of a link, colored by symmetric or exterior powers of the fundamental representation, is q-holonomic with respect to the color parameters. As a result, we obtain the existence of an (a,q) super-polynomial of all knots in 3-space. Our result has implications on the quantization of the SL(2,C) character variety of knots using ideal triangulations or the topological recursion, and motivates questions on the web approach to representation theory.
Cite
@article{arxiv.1211.6388,
title = {The colored HOMFLY polynomial is q-holonomic},
author = {Stavros Garoufalidis},
journal= {arXiv preprint arXiv:1211.6388},
year = {2012}
}
Comments
8 pages, 3 figures