New Solutions of the Yang-Baxter Equation Based on Root of 1 Representations of the Para-Bose Superalgebra U$_q$[osp(1/2)]

Abstract

New solutions of the quantum Yang-Baxter equation, depending in general on three arbitrary parameters, are written down. They are based on the root of unity representations of the quantum orthosymplectic superalgebra \\U, which were found recently. Representations of the braid group $B_N$ are defined within any $N^{th}$ tensorial power of root of 1 \\U modules.