An Ade-O Classification of Minimal Incompressible Quantum Hall Fluids
  We briefly review a theoretical picture of the quantum Hall effect in which gauge symmetry of non-relativistic quantum mechanics, the representation theory of U(1)-current algebra, and the study of odd, positive integral quadratic forms on N-dimensional integral lattices play fundamental roles. We present a classification of so-called minimal incompressible quantum Hall fluids for low values of the lattice dimension N. The classification contains several new universality classes of quantum Hall fluids which are physically interesting. 
J\"urg Fr\"ohlich, Urban M. Studer, and Emmanuel Thiran