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In this paper we elaborate on the correspondence between the quantum Hall
system with filling factor equal to one and the N=4 SYM theory in the 1/2
BPS sector, previously mentioned in the [hep-th/0409174, hep-th/0409115].
We show the equivalence of the two in various formulations of the quantum
Hall physics. We present an extension of the noncommutative Chern-Simons
Matrix theory which contains independent degrees of freedom (fields) for
particles and quasiholes. The BPS configurations of our model, which is a
model with explicit particle-quasihole symmetry, are in one-to-one
correspondence with the 1/2 BPS states in the N=4 SYM. Within our model we
shed light on some less clear aspects of the physics of the N=4 theory in
the 1/2 BPS sector, like the giant dual-giant symmetry, stability of the
giant gravitons, and stringy exclusion principle and possible implications
of the (fractional) quantum Hall effect for the AdS/CFT correspondence.
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