Colored knot polynomials for Pretzel knots and links of arbitrary genus

Abstract

A very simple expression is conjectured for arbitrary colored Jones and HOMFLY polynomials of a rich $(g+1)$-parametric family of Pretzel knots and links. The answer for the Jones and HOMFLY polynomials is fully and explicitly expressed through the Racah matrix of U_q(SU_N), and looks related to a modular transformation of toric conformal block.

5 pages

References in corpus (5)

• HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
• Character expansion for HOMFLY polynomials. III. All 3-Strand braids in the first symmetric representation
• Eigenvalue hypothesis for Racah matrices and HOMFLY polynomials for 3-strand knots in any symmetric and antisymmetric representations
• Reformulated invariants for non-torus knots and links
• Wall Crossing Invariants: from quantum mechanics to knots

Cited by in corpus (15)

• Correlators in tensor models from character calculus
• On rectangular HOMFLY for twist knots
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
• Differential expansion for link polynomials
• On R-matrix approaches to knot invariants
• On moduli space of symmetric orthogonal matrices and exclusive Racah matrix $\bar{S}$ for representation $R=[3,1]$ with multiplicities
• New symmetries for the $U_q(s{l}_N)$ 6-j symbols from the Eigenvalue conjecture
• Extension of KNTZ trick to non-rectangular representations
• On exclusive Racah matrices $\bar{S}$ for rectangular representations
• Gaussian distribution of LMOV numbers
• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$
• Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalism
• On geometric bases for A-polynomials II: ${\mathfrak{su}}_3$ and Kuberberg bracket
• HOMFLY Polynomials of Pretzel Knots
• On an alternative stratification of knots