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arXiv · 1811.07538

Bi-partite vertex model and multi-colored link invariants

Saswati Dhara·Romesh K. Kaul·P. Ramadevi·Vivek Kumar Singh
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Abstract

Construction of representations of braid group generators from $N$-state vertex models provide an elegant route to study knot and link invariants. Using such a braid group representation, an algebraic formula for the link invariants was put forth when the same spin $(N-1)/2$ are placed on all the component knots. In this paper, we generalise the procedure to deduce representations of braiding generators from bi-partite vertex models. Such a representation allows the study of multi-colored link invariants where the component knots carry different spins. We propose a multi-colored link invariant formula in terms of braiding generators derived from $R$ matrices of bi-partite vertex models.

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Saswati Dhara, Romesh K. Kaul, P. Ramadevi, Vivek Kumar Singh. 2018-11-19. Bi-partite vertex model and multi-colored link invariants. https://arxiv.org/abs/1811.07538

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