Algebraic Approach to Fractional Quantum Hall Effect

We construct an algebraic description for the ground state and for the static response of the quantum Hall plateaux with filling factor $\nu =N\mathrm{/}(2N+1)$ in the large $N$ limit. By analyzing the algebra of the fluctuations of the shape of the Fermi surface of the composite fermions, we find the explicit form of the projected static structure factor at large $N$ and fixed $z=(2N+1) q\ell_B\sim 1$\mathrm{.}When$z<3.8$, the result does not depend on the particular form of the Hamiltonian.