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arXiv · 1805.03916

Multi-Colored Links From 3-strand Braids Carrying Arbitrary Symmetric Representations

Saswati Dhara·A. Mironov·A. Morozov·An. Morozov·P. Ramadevi·Vivek Kumar Singh·A. Sleptsov
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Abstract

Obtaining colored HOMFLY-PT polynomials for knots from 3-strand braid carrying arbitrary $SU(N)$ representation is still tedious. For a class of rank $r$ symmetric representations, $[r]$-colored HOMFLY-PT $H_{[r]}$ evaluation becomes simpler. Recently it was shown that $H_{[r]}$, for such knots from 3-strand braid, can be constructed using the quantum Racah coefficients (6j-symbols) of $U_q(sl_2)$. In this paper, we generalise it to links whose components carry different symmetric representations. We illustrate the technique by evaluating multi-colored link polynomials $H_{[r_1],[r_2]}$ for the two-component link L7a3 whose components carry $[r_1]$ and $[r_2]$ colors.

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BibTeXRIS

Saswati Dhara, A. Mironov, A. Morozov, An. Morozov, P. Ramadevi, Vivek Kumar Singh, A. Sleptsov. 2018-05-10. Multi-Colored Links From 3-strand Braids Carrying Arbitrary Symmetric Representations. https://doi.org/10.1007/s00023-019-00841-z

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