Commutators of Jastrow Factors and Angular Momentum Operators

We present detailed calculations of commutators of the Jastrow factor and certain differential operators useful in the fractional quantum Hall effect. In particular, we analyze action of the angular momentum operators projected from the Haldane sphere on an arbitrary composite fermions state. Examined L⁺ and L¯ momentum operators and following uniformity condition had proven to be useful in the search for candidates for quantum Hall ground states among many families of polynomials including the Jack polynomials.