REPRESENTATIONS OF THE QUANTUM MATRIX ALGEBRA M(Q,P)(2)

It is shown that the finite dimensional irreducible representations of the quantum matrix algebra M(q,p)(2) (the coordinate ring of GL(q,p)(2)) exist only when both q and p are roots of unity. In this case the space of states has either the topology of a torus or a cylinder, which may be thought of as generalizations of cyclic representations.