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

We consider the irreducible highest-weight finite-dimensional representations of the quantum algebra U_q[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.