Composite fermions from the algebraic point of view

Composite fermion wavefuctions have been used to describe electrons in a strong magnetic field. We show that the polynomial part of these wavefunctions can be obtained by applying a normal ordered product of suitably defined annihilation and creation operators to an even power of the Vandermonde determinant, which can been considered as a kind of a non-trivial Fermi sea. In the case of the harmonic interaction we solve the system exactly in the lowest Landau level. The solution makes explicit the boson-fermion correspondence proposed recently.