Finite Noncommutative Chern-Simons with a Wilson Line and the Quantum Hall Effect

We present a finite dimensional matrix model associated to the noncommutative Chern-Simons theory, obtained by inserting a Wilson line. For a specific choice of the representation of the Wilson line the model is equivalent to the minimal modification of the matrix model which is compatible with finite dimensional matrices, and was introduced previously to study droplets of quantum Hall fluid. For other representations we obtain generalizations corresponding to regularized U(n) Chern-Simons theoris, representing multilayered quantum Hall fluids.