More on U q(su(1,1)) with q a root of unity

Abstract

Highest weight representations of U q (su(1, 1)) with q = exp πi/N are investigated. The structures of the irreducible hieghesat weight modules are discussed in detail. The Clebsch-Gordan decomposition for the tensor product of two irreducible representations is discussed. By using the results, a representation of SL(2, R) ⊗ U q (su(2)) is also presented in terms of holomorphic sections which also have U q (su(2)) index. Furthermore we realise Z N -graded supersymmetry in terms of the representation. An explicit realization of Osp(1|2) via the heighest weight representation of U q (su(1, 1)) with q 2 = −1 is given.