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Representations for quantum groups at q an Nth root of 1 with a structure resembling the algebraic structure in the theory of the chiral Potts models are constructed in the Uq(sp(2n,C)), Uq(so(2n+1,C)), and Uq(so(2n,C)) cases. The dimensions of the given representations and their number of free parameters are N(1/2)(dim g-rank g), dim g, respectively.

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Representations of Quantum Groups U ε (g n ), g n any semi simple Lie algebra of rank n, are constructed from arbitrary representations of rank n − 1 quantum groups for ε a root of unity. Representations which have the maximal dimension and number of free parameters for irreducible representations arise as special cases.