KNIZHNIK-ZAMOLODCHIKOV EQUATION AND EXTENDED SYMMETRY FOR STABLE HALLSTATES

We describe an n-component Abelian Hall fluid as a system of composite bosons moving in an average null field given by the external magnetic field and by the statistical flux tubes located at the position of th e particles. The collective vacuum state, in which the bosons condense d, is characterized by a Knizhnik-Zamolodchikov differential equation relative to a U(1)(n) Wess-Zumino model. In the case of states belongi ng to Jain's sequences the Knizhnik-Zamolodchikov equation naturally l eads to the presence of a U(1) x SU(n) extended algebra. Only the U(I) mode is charged while the SU(n) modes are neutral, in agreement with recent results obtained in the study of the edge states.