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.
