Colored HOMFLY polynomial via skein theory

Abstract

In this paper, we study the properties of the colored HOMFLY polynomials via HOMFLY skein theory. We prove some limit behaviors and symmetries of the colored HOMFLY polynomial predicted in some physicists' recent works.

21 pages, 3 figures

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Cited by in corpus (16)

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• HOMFLY polynomials in representation [3,1] for 3-strand braids
• Cabling procedure for the colored HOMFLY polynomials
• Rectangular superpolynomials for the figure-eight knot
• Torus knot polynomials and susy Wilson loops
• A new symmetry of the colored Alexander polynomial
• Differential Expansion for antiparallel triple pretzels: the way the factorization is deformed
• $S$-Functions, Spectral Functions of Hyperbolic Geometry, and Vertex Operators with Applications to Structure for Weyl and Orthogonal Group Invariants
• On explicit formulae of LMOV invariants
• Defect and degree of the Alexander polynomial
• A novel symmetry of colored HOMFLY polynomials coming from $\mathfrak{sl}(N|M)$ superalgebras
• Torus knots in adjoint representation and Vogel's universality
• Direct proof of one-hook scaling property for Alexander polynomial from Reshetikhin-Turaev formalism