  We describe a $n$ component abelian Hall fluid as a system of {\it 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 the particles. The
collective vacuum state, in which the bosons condense, is characterized by a
Knizhnik-Zamolodchikov differential equation relative to a $\hat {U}(1)^n$
Wess-Zumino model. In the case of states belonging to Jain's sequences the
Knizhnik-Zamolodchikov equation naturally leads to the presence of an
$\hat{U}(1)\ot \hat{SU}(n)$ extended algebra. Only the $\hat{U}(1)$ mode is
charged while the $\hat{SU}(n)$ modes are neutral, in agreement with recent
results obtained in the study of the edge states.

Condensed Matter