We propose a matrix model to describe a class of fractional quantum Hall
(FQH) states for a system of (N_1+N_2) electrons with filling factor more
general than in the Laughlin case. Our model, which is developed for FQH states
with filling factor of the form \nu_{k_1k_2}=\frac{k_1+k_2}{k_1k_2} (k_1 and
k_2 odd integers), has a U(N_1)\times U(N_2) gauge invariance, assumes that FQH
fluids are composed of coupled branches of the Laughlin type, and uses ideas
borrowed from hierarchy scenarios. Interactions are carried, amongst others, by
fields in the bi-fundamentals of the gauge group. They simultaneously play the
role of a regulator, exactly as does the Polychronakos field. We build the
vacuum configurations for FQH states with filling factors given by the series
\nu_{p_1p_2}=\frac{p_2}{p_1p_2-1}, p_1 and p_2 integers. Electrons are
interpreted as a condensate of fractional D0-branes and the usual degeneracy of
the fundamental state is shown to be lifted by the non-commutative geometry
behaviour of the plane. The formalism is illustrated for the state at
\nu={2/5}.Comment: 40 pages, 1 figure, clarifications and references adde
