Polynomial GL, Yang-Baxter Equation and Quantum Group SL(2)q

Abstract

In this paper, we define the polynomial G(L) by way of the braids. We construct the abstract tensor model of the polynomial G(L) and we obtain the new solutions relevant with the state model of the polynomial G(L) to the Yang-Baxter equation. We also construct the vacuum-vacuum expectation model of the polynomial G(L) and we show that the studies performed using the Kaufmann bracket on the quantum group SL(2)(q) with q = A(2) are valid for the state model of the polynomial G(L) without q = A(2).