CENTER AND REPRESENTATIONS OF SMALL QUANTUM SUPERALGEBRAS AT ROOTS OFUNITY

When the deformation parameter is a root of unity, the centre of a qua ntum group can be described by a set of generators and non trivial rel ations. In the case of U-q(sl(N)), these relations simply derive from the expressions of the deformed Casimir operators. In the case of U-q( osp(1\2)), the relation is simple if we ise an operator which anticomm utes with the fermionic generators and whose square is the quadratic C asimir. This operator also simplifies the classification of finite dim ensional irreducible representations. In the case of U-q(sl(1\2)), the relations derive from the (infinite set of) standard Casimir operator s.