On rectangular HOMFLY for twist knots

Abstract

As a new step in the study of rectangularly-colored knot polynomials, we reformulate the prescription of arXiv:1606.06015 for twist knots in the double-column representations $R=[rr]$ in terms of skew Schur polynomials. These, however, are mysteriously shifted from the standard topological locus, what makes further generalization to arbitrary $R=[r^s]$ not quite straightforward.

6 pages

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Cited by in corpus (19)

• Nimble evolution for pretzel Khovanov polynomials
• Differential expansion for link polynomials
• On moduli space of symmetric orthogonal matrices and exclusive Racah matrix $\bar{S}$ for representation $R=[3,1]$ with multiplicities
• Perspectives of differential expansion
• Extension of KNTZ trick to non-rectangular representations
• Knot polynomials for twist satellites
• Factorization of differential expansion for non-rectangular representations
• On exclusive Racah matrices $\bar{S}$ for rectangular representations
• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$
• Planar decomposition of the HOMFLY polynomial for bipartite knots and links
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• Towards tangle calculus for Khovanov polynomials
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• Generalized hypergeometric series for Racah matrices in rectangular representations
• Evolution properties of the knot's defect
• Defect and degree of the Alexander polynomial