  The electronic excitations at the edges of a Hall bar not much wider than a
few magnetic lengths are studied theoretically at filling $\nu = 2$. Both
mean-field theory and Luttinger liquid theory techniques are employed for the
case of a null Zeeman energy splitting. The first calculation yields a stable
spin-density wave state along the bar, while the second one predicts dominant
Wigner-crystal correlations along the edges of the bar. We propose an
antiferromagnetic Wigner-crystal groundstate for the edge electrons that
reconciles the two results. A net Zeeman splitting is found to produce canting
of the antiferromagnetic order.
