FQHE AND JAINS APPROACH ON THE TORUS

By using the explicit knowledge of the lowest energy single particle w ave functions in the presence of an arbitrary magnetic field, we exten d to the case of a torus Jain's idea of looking at the FQHE as a manif estation of an integer effect for composite fermions. We show that thi s can be realized thanks to a redefinition of the vacuum state that is explicitly collective in nature. We also discuss the relationship of this approach with the hierarchical scheme and with the characterizati on of the Hall states in terms of W-1+infinity algebras and 2D conform al field theories.