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The colored HOMFLYPT function is $q$-holonomic

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arxiv 1604.08502 v2 pith:NP4V75G5 submitted 2016-04-28 math.GT hep-th

Stavros Garoufalidis , Aaron D. Lauda , Thang T.Q. Lê This is my paper · ORCID
classification math.GThep-th
keywords coloredfunctionholonomichomflyptknotsnumberauxiliarycase
verification ladder T0 review T1 audit T2 compute T3 formal
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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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