Scientific article
Open access

A new solution to the star-triangle equation based on Uq(sl(2)) at roots of unity

Published inNuclear Physics. B, vol. 373, no. 3, p. 761-778
Publication date1992

We find new solutions to the Yang-Baxter equation in terms of the interwiner matrix for semi-cyclic representations of the quantum group Uq(sl(2)) with q = e2πi/N. These interwiners serve to define the Boltzmann weights of a lattice model, which shares some similarities with the chiral Potts model. An alternative interpretation of these Boltzmann weights is as scattering matrices of solitonic structures whise kinematics is entirely governed by the quantum group. Finally, we consider the limit N → ∞ where we find an infinite-dimensional representation of the braid group, which may give rise to an invariant of knots and links.

Citation (ISO format)
GÓMEZ, César, SIERRA, Germán. A new solution to the star-triangle equation based on U<sub>q</sub>(sl(2)) at roots of unity. In: Nuclear Physics. B, 1992, vol. 373, n° 3, p. 761–778. doi: 10.1016/0550-3213(92)90275-G
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ISSN of the journal0550-3213

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