PERIODIC AND PARTIALLY PERIODIC REPRESENTATIONS OF SU(N)Q

The Gelfand-Zetlin basis is adapted to SU(N)q for q a root of unit. Extra parameters are incorporated in the matrix elements of the generators to obtain all the invariants corresponding to the augmented center. A crucial identity is derived and proved, which guarantees the periodicity of the action of the generators. Full periodicity is relaxed by stages, some raising and lowering operators remaining injective while others become nilpotent with corresponding changes in the dimension of the representation. In the extreme case of highest weight representations, all the raising and lowering operators are nilpotent. As an alternative approach an auxiliary algebra giving all the periodic representations is presented. An explicit solution of this system for N = 3, while fully equivalent to the G.-Z. basis, turns out to be much simpler.