REPRESENTATIONS OF QUANTUM SO(8) AND RELATED QUANTUM ALGEBRAS

We study irreducible representations of the quantum group U(epsilon)(s o(8)) when epsilon is-an-element-of C is a primitive l(th) root of un ity. By a theorem of De Concini and Kac, there is a finite number of s uch representations associated to each point of a complex algebraic va riety of dimension 28 and the generic representation has dimension l12 . We give explicit constructions of essentially all the irreducible re presentations whose dimension is divisible by l8. In addition, we cons truct all cyclic representations of minimal dimension. This minimal di mension is l5, in accordance with a conjecture of De Concini, Kac and Procesi.