THE MASSLESS REPRESENTATIONS OF THE CONFORMAL QUANTUM ALGEBRA

The massless representations of the conformal quantum algebra U(q)(su( 2, 2)) for complex q such that Absolute value of q = 1 are studied in detail. By factorizing out all singular vectors of the corresponding V erma modules, a simple basis for these representations is explicitly c onstructed. This basis is new also for the usual conformal algebra su( 2, 2). This construction allows a straightforward treatment of the cas e q a root of unity, when the representations are unitary and finite-d imensional.