Jain states on a torus: an unifying description

We analyze the modular properties of the effective CFT description for Jain plateaux corresponding to the fillings nu=m/(2pm+1). We construct its characters for the twisted and the untwisted sector and the diagonal partition function. We show that the degrees of freedom entering the partition function go to complete a Zm-orbifold construction of the RCFT U(1) x SU(m) proposed for the Jain states. The resulting extended algebra of the chiral primary fields can be also viewed as a RCFT extension of the U(1) x W(m) minimal models. For m=2 we prove that our model, the TM, gives the RCFT closure of the extended minimal models U(1) x W(2). (author)