Yang-Baxterization of braid group representations

Abstract

For a given braid group representation (BGR), a process of the Yang-Baxterization is formulated to generate solutions of the Yang-Baxter equation (YBE). When a BGR admits the Birman-Wenzl (BW) algebraic structure, this process can be explicitly passed through and two types of trigonometric solutions of YBE are generated from such a BGR. These two solutions have, the essential difference to each other and both of them, preserve the crossing symmetry property if the given BGR has. By taking certain, reduction on the BW algebra, the rational solution is also generated. A practical condition to judge whether a BGR satisfies the BW algebra is given, from which one finds that not only the familiar BGRs of [5,7,9], but also some new, ones obtained recently in [12] have the BW structure. Thus they can be explicitly Yang-Baxterized to solutions of the YBE.