TRANSITION FROM SU(2)(L)XSU(2)(R)XU(1)(B-L) REPRESENTATION TO SU(2)(L)XU(1)(Y) BY Q-DEFORMATION AND THE CORRESPONDING CLASSICAL BREAKING TERM OF CHIRAL U(2)

The minimal Standard Model exhibits a nontrivial chiral U(2) symmetry if the VEV and the hyperchange splitting Delta = (y(R)(u)-y(R)(d))/2 of right-handed leptons (quarks) in a family vanish and Q=T-0+Y independently in each helicity sector. As a generalization, we start with SU(2)(L)xSU(2)(R)xU(1)((B-L)) and introduce Delta as a continuous parameter which is a measure of explicit symmetry breakdown. Values 0 less than or equal to Delta less than or equal to 1/2 take the neutral generator of the isospin-1/2 representation to the singlet representation, i.e. 'deformes' the LR representation into the minimal Standard one. The corresponding classical 0(3)-breaking term is a magnetic field perpendicular to the x(3),-axis. A simple mapping on the fundamental Drinfeld-Jimbo q-deformed SU(2) representation is given.