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arXiv · 2005.01188

A novel symmetry of colored HOMFLY polynomials coming from $\mathfrak{sl}(N|M)$ superalgebras

V. Mishnyakov·A. Sleptsov·N. Tselousov
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Abstract

We present a novel symmetry of the colored HOMFLY polynomial. It relates pairs of polynomials colored by different representations at specific values of $N$ and generalizes the previously known "tug-the-hook" symmetry of the colored Alexander polynomial. As we show, the symmetry has a superalgebra origin, which we discuss qualitatively. Our main focus are the constraints that such a property imposes on the general group-theoretical structure, namely the $\mathfrak{sl}(N)$ weight system, arising in the perturbative expansion of the invariant. Finally, we demonstrate its tight relation to the eigenvalue conjecture.

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V. Mishnyakov, A. Sleptsov, N. Tselousov. 2020-05-03. A novel symmetry of colored HOMFLY polynomials coming from $\mathfrak{sl}(N|M)$ superalgebras. https://doi.org/10.1007/s00220-021-04073-3

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