Laughlin states on the Poincare half-plane and its quantum group   symmetry
  We find the Laughlin states of the electrons on the Poincare half-plane in different representations. In each case we show that there exist a quantum group $su_q(2)$ symmetry such that the Laughlin states are a representation of it. We calculate the corresponding filling factor by using the plasma analogy of the FQHE. 
M. Alimohammadi and H. Mohseni Sadjadi