Exotic Bialgebra S03: Representations, Baxterisation and Applications

The exotic bialgebra S03, defined by a solution of the Yang–Baxter equation, which is not a deformation of the trivial, is considered. Its FRT dual algebra s03F is studied. The Baxterisation of the dual algebra is given in two different parametrizations. The finite-dimensional representations of s03F are considered. Diagonalizations of the braid matrices are used to yield remarkable insights concerning representations of the L-algebra and to formulate the fusion of finite-dimensional representations. Possible applications are considered, in particular, an exotic eight-vertex model and an integrable spin-chain model.