CHINESE ACAD SCI, GRAD SCH, BEIJING 100039, PEOPLES R CHINA
; CHINESE CTR ADV SCI & TECHNOL, WORLD LAB, BEIJING 100080, PEOPLES R CHINA
; INST HIGH ENERGY PHYS, BEIJING 100039, PEOPLES R CHINA
In the decomposition of a coproduct in the direct product of two irreducible representation spaces of the quantum enveloping algebra U(q)sl(2), the mixed representation, reducible but indecomposable, appears when q is a root of unity. In this paper, the necessary and sufficient condition for mixture of two irreducible representations are presented, the quantum Clebsch-Gordan coefficients which are neither all vanishing nor divergent for the non-generic q values are defined, and the method for computing the new states are discussed in some detail.