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

References in corpus (3)

• HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
• Colored knot polynomials for Pretzel knots and links of arbitrary genus
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY

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• Planar decomposition of the HOMFLY polynomial for bipartite knots and links
• On $6j$-symbols for symmetric representations of $U_q({\mathfrak{su}}_N)$
• Towards tangle calculus for Khovanov polynomials
• Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed
• Defect and degree of the Alexander polynomial
• Evolution properties of the knot's defect