THE COLORED HOMFLY POLYNOMIAL IS q-HOLONOMIC
نویسنده
چکیده
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.
منابع مشابه
ar X iv : m at h / 06 01 26 6 v 1 [ m at h . Q A ] 1 1 Ja n 20 06 ON THE HECKE ALGEBRAS AND THE COLORED HOMFLY POLYNOMIAL
Abstract. The colored HOMFLY polynomial is the quantum invariant of oriented links in S associated with irreducible representations of the quantum group Uq(slN). In this paper, using an approach to calculate quantum invariants of links via cabling-projection rule, we derive a formula for the colored HOMFLY polynomial in terms of the characters of the Hecke algebras and Schur polynomials. The te...
متن کاملThe colored Jones function is q–holonomic
A function of several variables is called holonomic if, roughly speaking, it is determined from finitely many of its values via finitely many linear recursion relations with polynomial coefficients. Zeilberger was the first to notice that the abstract notion of holonomicity can be applied to verify, in a systematic and computerized way, combinatorial identities among special functions. Using a ...
متن کامل1 1 Ja n 20 06 ON THE HECKE ALGEBRAS AND THE COLORED HOMFLY POLYNOMIAL
Abstract. The colored HOMFLY polynomial is the quantum invariant of oriented links in S associated with irreducible representations of the quantum group Uq(slN). In this paper, using an approach to calculate quantum invariants of links via cabling-projection rule, we derive a formula for the colored HOMFLY polynomial in terms of the characters of the Hecke algebras and Schur polynomials. The te...
متن کاملTHE sl3 JONES POLYNOMIAL OF THE TREFOIL: A CASE STUDY OF q-HOLONOMIC SEQUENCES
The sl3 colored Jones polynomial of the trefoil knot is a q-holonomic sequence of two variables with natural origin, namely quantum topology. The paper presents an explicit set of generators for the annihilator ideal of this q-holonomic sequence as a case study. On the one hand, our results are new and useful to quantum topology: this is the first example of a rank 2 Lie algebra computation con...
متن کاملOn a Deformed Topological Vertex
Recall the topological vertex involves three partitions, when one of them is empty it is related to the leading term of the large N colored HOMFLY polynomials of the Hopf link, and the general topological vertex can be expressed in terms of such leading terms. We will use the whole colored HOMFLY polynomials to define the deformed vertex, hence deformations of the partition functions of topolog...
متن کامل