Dressing symmetry of the Zhiber-Mikhailov-Shabat model

The dressing symmetry of the most typical example among the twist affine Toda field theories-the Zhiber-Mikhailov-Shabat model - is carefully analyzed. By factorizing the group of dressing transformations we find that there exists a non-trivial Poisson structure on the parameter space of the dressing group, which is built by the semi-classical deformation of the loop algebra A2(2). As an auxiliary product we also obtain the classical r-matrix of the Zhiber-Mikhailov-Shabat model. Finally, we argue how one should quantize an integrable system with the symmetric group of dressing transformations.