  Many bosonic (fermionic) fractional quantum Hall states, such as Laughlin,
Moore-Read and Read-Rezayi wavefunctions, belong to a special class of
orthogonal polynomials: the Jack polynomials (times a Vandermonde determinant).
This fundamental observation allows to point out two different recurrence
relations for the coefficients of the permanent (Slater) decomposition of the
bosonic (fermionic) states. Here we provide an explicit Fock space
representation for these wavefunctions by introducing a two-body squeezing
operator which represents them as a Jastrow operator applied to reference
states, which are in general simple periodic one dimensional patterns.
Remarkably, this operator representation is the same for bosons and fermions,
and the different nature of the two recurrence relations is an outcome of
particle statistics.
