The colored HOMFLY polynomial is q-holonomic

Stavros Garoufalidis

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arXiv · 1211.6388

The colored HOMFLY polynomial is q-holonomic

Stavros Garoufalidis

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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.

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Stavros Garoufalidis. 2012-11-27. The colored HOMFLY polynomial is q-holonomic. https://arxiv.org/abs/1211.6388

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