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 Z_{m}-orbifold construction of the RCFT U(1)xSU(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)xW(m) minimal models. For m=2 we prove that our model, the TM, gives the RCFT closure of the extended minimal models U(1)xW(2).