Representations of the quantum group GL q(2) for values of q on the unit circle

Abstract

We construct finite dimensional matrix representations of the quantum group GL q (2, C ) for values of the deformation parameter q= exp(2π iλ), λϵ R . When λ=1/ N, N being a prime integer, using the representations of the Heisenberg group algebra we construct N-dimensional matrix representations of GL q (2, C ) which can be used as building blocks for representations with q being a rational number. For the case where λ is a real irrational number we provide some examples of the generators of GL q (2, C ).