Yang-Baxter Equation for $A^{(1)}_{n-1}$ Broken ${\Bf Z}_N $ Models

TL;DR

This paper constructs a new solvable model generalizing the broken Z_N model using the gl_n-Sklyanin algebra and proves its Yang-Baxter equation, advancing integrable systems theory.

Contribution

It introduces a novel sl_n-generalization of the broken Z_N model via a new algebraic construction and verifies its integrability.

Findings

Established a factorized representation of the gl_n-Sklyanin algebra.

Derived a new solvable model generalizing the broken Z_N model.

Proved the Yang-Baxter equation for the new model.

Abstract

We construct a factorized representation of the $\frak g \frak l _n$-Sklyanin algebra from the vertex-face correspondence. Using this representation, we obtain a new solvable model which gives an $\frak s \frak l _n$-generalization of the broken $\bz _N $ model. We further prove the Yang-Baxter equation for this model.