Composite particles and the eigenstates of Calogero-Sutherland and Ruijs']jsenaars-Schneider

We establish a one-to-one correspondence between the "composite particles" with N particles and the Young tableaux with at most N rows. We apply this correspondence to the models of Calogero-Sutherland and Ruijsenaars-Schneider and we obtain a momentum space representation of the "composite particles" in terms of creation operators attached to the Young tableaux. Using the technique of bosonization, we obtain a position space representation of the "composite particles" in terms of products of vertex operators. In the special case where the "composite particles" are bosons and if we add one extra quasiparticle or quasihole, we construct the ground state wave functions corresponding to the Jain series nu =p/(2np +/-1) of the fractional quantum Hall effect. (C) 2000 American Institute of Physics. [S0022-2488(00)04307-3].