An analytically solvable few-electron model of a double-layer electron system is presented which includes mixing with all Landau levels. Inter-layer correlations are found to give rise to novel ground states which differ fundamentally from previously suggested Jastrow-like wavefunctions for double layer N-electron systems. Comparison with experimental data suggests that these states may represent small-N precursors of recently observed fractional quantum Hall states in double-layer (large-N) systems.
We study topological order and edge excitations of the \ensuremath{\nu}=1/2 fractional quantum Hall state (FQH) of spin polarized electrons in a single-layer system. We find that the 1/2 FQH state obtained in the numerical study of Greiter et al. has a non-Abelian topological order suggested by Moore and Read. The edge excitations in such a non-Abelian FQH state are found to be described by the U(1) Kac-Moody algebra plus a chiral Majorana fermion theory. The electron and the quasiparticle propagators are calculated. Some experimental consequences are also discussed.