  We consider a large collection of particles obeying $A_r$ statistics. The
system behaves like a quantum droplet characterized by a constant Husimi
distribution. We show that the excitations of this system live on the boundary
of the droplet and they are described by an effective chiral boson action
generalizing the Wess-Zumino-Witten theory in two dimension. Our analysis is
based on the Fock-Bargmann analytical representations associated to $A_r$
statistics. The quantization of the theory describing the dynamics on the edge
is achieved. As by product, we prove that the edge excitations are given by a
tensorial product of $r$ abelian bosonic fields.
