Polynomial relations in the centre ofU q (sl(N))

When the parameter of deformationq is a root of unity, the centre ofU _q (sl(N)) contains, besides the usualq-deformed Casimirs, a set of new generators, which are basically themth powers of all the Cartan generators ofU _q (sl(N)). All these central elements are, however, not independent. In this Letter, generalizing the well-known case ofU _q (sl(2)), we explicitly write polynomial relations satisfied by the generators of the centre. Application to the parametrization of irreducible representations and to fusion rules are sketched.On leave from SPht, CE Saclay, 91191 Gif-sur-Yvette Cedex, France.