On U h ( sl ( 2 ) ) , U h ( e ( 3 ) ) and their Representations

By solving a set of recursion relations for the matrix elements of the Uh(sl(2)) generators, the finite dimensional highest weight representations of the algebra were obtained as factor representations. Taking a nonlinear combination of the generators of the two copies of the Uh(sl(2)) algebra, we obtained Uh(so(4)) algebra. The latter, on contraction, yields Uh(e(3)) algebra. A nonlinear map of Uh(e(3)) algebra on its classical analogue e(3) was obtained. The inverse mapping was found to be singular. It signifies a physically interesting situation, where in the momentum basis, a restricted domain of the eigenvalues of the classical operators is mapped on the whole real domain of the eigenvalues of the deformed operators. [email protected] [email protected] Permanent address: Department of Theoretical Physics, University of Madras, Guindy Campus, Madras600025, India Laboratoire Propre du CNRS UPR A.0014