  We study a U(N) gauged matrix quantum mechanics which, in the large N limit,
is closely related to the chiral WZW conformal field theory. This manifests
itself in two ways. First, we construct the left-moving Kac-Moody algebra from
matrix degrees of freedom. Secondly, we compute the partition function of the
matrix model in terms of Schur and Kostka polynomials and show that, in the
large $N$ limit, it coincides with the partition function of the WZW model.
This same matrix model was recently shown to describe non-Abelian quantum Hall
states and the relationship to the WZW model can be understood in this
framework.
