Primitive Ideals of Cq(SL(n)) Original Research Article

The primitive ideals of the quantum group Cq[SL(n)] are classified in the case where q is a non-zero complex number which is not a root of unity. It is shown that the orbits in Prim Cq[SL(n)] under the action of the character group H congruent with (C*)n−1 are parameterized naturally by W × W where W is the associated Weyl group. It is shown that there is a natural one-to-one correspondence between primitive ideals of Cq[SL(n)] and symplectic leaves of the associated Poisson algebraic group SL(n, C).