Special colored Superpolynomials and their representation-dependence

Abstract

We introduce the notion of "special superpolynomials" by putting q=1 in the formulas for reduced superpolynomials. In this way we obtain a generalization of special HOMFLY polynomials depending on one extra parameter t. Special HOMFLY are known to depend on representation R in especially simple way: as |R|-th power of the fundamental ones. We show that the same dependence persists for our special superpolynomials in the case of symmetric representations, at least for the 2-strand torus and figure-eight knots. For antisymmetric representations the same is true, but for t=1 and arbitrary q. It would be interesting to find an interpolation between these two relations for arbitrary representations, but no superpolynomails are yet available in this case.

5 pages

References in corpus (3)

• The Refined Topological Vertex
• HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations
• Super-A-polynomials for Twist Knots

Cited by in corpus (10)

• Colored HOMFLY polynomials of knots presented as double fat diagrams
• Colored HOMFLY polynomials for the pretzel knots and links
• Differential hierarchy and additional grading of knot polynomials
• Towards R-matrix construction of Khovanov-Rozansky polynomials. I. Primary $T$-deformation of HOMFLY
• Colored Kauffman Homology and Super-A-polynomials
• HOMFLY polynomials in representation [3,1] for 3-strand braids
• Cabling procedure for the colored HOMFLY polynomials
• Eigenvalue conjecture and colored Alexander polynomials
• Rectangular superpolynomials for the figure-eight knot
• On possible existence of HOMFLY polynomials for virtual knots