CENTER AND REPRESENTATIONS OF U-Q(SL(2-VERTICAL-BAR-1)) AT ROOTS OF UNITY

Quantum groups at the roots of unity have the property that their cent re is enlarged. Polynomial equations relate the standard deformed Casi mir operators and the new central elements. These relations are import ant from a physical point of view, since they correspond to relations between quantum expectation values of observables that have to be sati sfied on all physical states. In this paper, we establish these relati ons in the case of the quantum Lie superalgebra U-q (s1(2\1)). In the course of the argument, we find and use a set of representations such that any relation satisfied on all the representations of the set is t rue in U-q(sl(2\1)). This set is a subset of the set of all the finite -dimensional irreducible representations of U-q(sl(2\1)), which we cla ssify and describe explicitly.