Link polynomial calculus and the AENV conjecture

Abstract

Using the recently proposed differential hierarchy (Z-expansion) technique, we obtain a general expression for the HOMFLY polynomials in two arbitrary symmetric representations of link families, including Whitehead and Borromean links. Among other things, this allows us to check and confirm the recent conjecture of arXiv:1304.5778 that the large representation limit (the same as considered in the knot volume conjecture) of this quantity matches the prediction from mirror symmetry consideration. We also provide, using the evolution method, the HOMFLY polynomial in two arbitrary symmetric representations for an arbitrary member of the one-parametric family of 2-component 3-strand links, which includes the Hopf and Whitehead links.

20 pages

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Cited by in corpus (22)

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• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Sequencing BPS Spectra
• On the defect and stability of differential expansion
• HOMFLY polynomials in representation [3,1] for 3-strand braids
• Factorization of differential expansion for antiparallel double-braid knots
• On rectangular HOMFLY for twist knots
• Tangle blocks in the theory of link invariants
• Eigenvalue hypothesis for multi-strand braids
• Kerov functions revisited
• Checks of integrality properties in topological strings
• On Hopf-induced deformation of topological locus
• On possible existence of HOMFLY polynomials for virtual knots
• Quantum Racah matrices up to level 3 and multicolored link invariants
• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$
• Evolution method and HOMFLY polynomials for virtual knots
• On skew tau-functions in higher spin theory
• Pentad and triangular structures behind the Racah matrices
• On geometric bases for A-polynomials II: ${\mathfrak{su}}_3$ and Kuberberg bracket