Unitarity and irrationality for the quantum algebra Uq[SU(2)]

We consider the irreducible highest-weight finite-dimensional representations of the quantum algebra Uq[SU(2)], for q=exp(iπ/p0) with 2<p0<∞. We find that there are three classes of such representations, which are characterized by their parity: +1 (corresponding to unitary representations), -1, and no definite parity. The representations of definite parity have dimensions that are given by the Takahashi-Suzuki numbers corresponding to the value of p0. We suggest that these representations may be relevant for conformal field theory. (orig.)