  When the parameter of deformation q is a m-th root of unity, the centre of
U_q(sl(N))$ contains, besides the usual q-deformed Casimirs, a set of new
generators, which are basically the m-th powers of all the Cartan generators of
U_q(sl(N)). All these central elements are however not independent. In this
letter, generalising the well-known case of U_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.
