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arXiv · 1408.3076

On colored HOMFLY polynomials for twist knots

A. Mironov·A. Morozov·An. Morozov
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Abstract

Recent results of J.Gu and H.Jockers provide the lacking initial conditions for the evolution method in the case of the first non-trivially colored HOMFLY polynomials H_{[21]} for the family of twist knots. We describe this application of the evolution method, which finally allows one to penetrate through the wall between (anti)symmetric and non-rectangular representations for a whole family. We reveal the necessary deformation of the differential expansion, what, together with the recently suggested matrix model approach gives new opportunities to guess what it could be for a generic representation, at least for the family of twist knots.

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A. Mironov, A. Morozov, An. Morozov. 2014-09-03. On colored HOMFLY polynomials for twist knots. https://doi.org/10.1142/s0217732314501831

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