  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.
