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arXiv · 1604.08502

The colored HOMFLYPT function is $q$-holonomic

Stavros Garoufalidis·Aaron D. Lauda·Thang T. Q. Lê
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Abstract

We prove that the HOMFLYPT polynomial of a link, colored by partitions with a fixed number of rows is a $q$-holonomic function. Specializing to the case of knots colored by a partition with a single row, it proves the existence of an $(a,q)$ super-polynomial of knots in 3-space, as was conjectured by string theorists. Our proof uses skew Howe duality that reduces the evaluation of web diagrams and their ladders to a Poincare-Birkhoff-Witt computation of an auxiliary quantum group of rank the number of strings of the ladder diagram.

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Stavros Garoufalidis, Aaron D. Lauda, Thang T. Q. Lê. 2016-04-28. The colored HOMFLYPT function is $q$-holonomic. https://doi.org/10.1215/00127094-2017-0030

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