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arXiv · 2203.11704

Three-partite vertex model and knot invariants

T. K. Kassenova·P. Tsyba·O. Razina·R. Myrzakulov
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Abstract

This work is dedicated to the consideration of the construction of a representation of braid group generators from vertex models with $N$-states, which provides a great way to study the knot invariant. An algebraic formula is proposed for the knot invariant when different spins $(N-1)/2$ are located on all components of the knot. The work summarizes procedure outputting braid generator representations from three-partite vertex model. This representation made it possible to study the invariant of a knot with multi-colored links, where the components of the knot have different spins. The formula for the invariant of knot with a multi-colored link is studied from the point of view of the braid generators obtained from the $R$-matrices of three-partite vertex models. The resulting knot invariant $5_2$ corresponds to the Jones polynomial and HOMFLY-PT.

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T. K. Kassenova, P. Tsyba, O. Razina, R. Myrzakulov. 2022-03-22. Three-partite vertex model and knot invariants. https://doi.org/10.1016/j.physa.2022.127283

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