Three-partite vertex model and knot invariants

T.K. Kassenova, P.Yu. Tsyba, O.V. Razina and R. Myrzakulov

Physica A: Statistical Mechanics and its Applications, 2022, vol. 597, issue C

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 52 corresponds to the Jones polynomial and HOMFLY-PT.

Keywords: Vertex model; Braid group; Knots theory (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:597:y:2022:i:c:s0378437122002400

DOI: 10.1016/j.physa.2022.127283

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