Primitive ideals of C q [SL(3)]

The primitive ideals of the Hopf algebraC _q SL(3)] are classified. In particular it is shown that the orbits in PrimC _q SL(3)] under the action of the representation groupH C ^*×C ^* are parameterized naturally byW×W, whereW is the associated Weyl group. It is shown that there is a natural one-to-one correspondence between primitive ideals ofC _q SL(3)] and symplectic leaves of the associated Poisson algebraic groupSL(3,C).Partially supported by a grant from the N.S.A.