Lawrence Berkeley National Laboratory Recent Work Title

The Clebsch-Gordan series of the 0(2,1) group. and its covering group su(1,1) for all cases except that of the supplemental series are derived. The continuable ClebschGordan coefficients (.or equivalently, the Wigner coefficients) are explicitly expressed in terms of the generalized hy-pergeometric function 3F2 . The spectra in the decomposition of the product of the two principal series are discussed. The applications to the unitary irreducible representation of 0(2,2) are also studied. . . .