Clebsch-Gordan Coefficients for <em>U_q</em>(<em>su</em>(1,1)) and <em>U_q</em>(<em>sl</em>(2)), and Linearization Formula of Matrix Elements

Abstract

The tensor product of two representations of the discrete series and the limit of the discrete series of Uq(su(1,1)) is decomposed into the direct sum of irreducible components of Uq(sl(1,1)), and the Clebsch-Gordan coefficients with respect to this decomposition are computed in two ways. In some cases, the tensor product of an irreducible unitary representation of Uq(su(2)) and a representation of the discrete series of Uq(su(1,1)) is decomposed into the direct sum of irreducible components of Uq(sl(2)), and the Clebsch-Gordan coefficients with respect to this decomposition are calculated, too. Making use of these coefficients, the linearization formula of the matrix elements is obtained.