Quantum group symmetry of the Quantum Hall effect on the non-flat surfaces

Abstract

After showing that the magnetic translation operators are not the symmetries of the QHE on non-flat surfaces , we show that there exist another set of operators which leads to the quantum group symmetries for some of these surfaces . As a first example we show that the $su(2)$ symmetry of the QHE on sphere leads to $s{u}_q(2)$ algebra in the equator . We explain this result by a contraction of $su(2)$ . Secondly , with the help of the symmetry operators of QHE on the Pioncare upper half plane , we will show that the ground state wave functions form a representation of the $s{u}_q(2)$ algebra .

8 pages,latex,no figure

References in corpus (6)

• W-Infinity and String Theory
• Quantum mechanics and quantum Hall effect on Riemann surfaces
• Area-preserving diffeomorphisms, W_{\infty} and $U_{q}(sl(2)) in Chern-Simons theory and Quantum Hall system
• Landau Levels and Quantum Group
• Quantum Group Symmetry and Quantum Hall Wavefunctions on a Torus
• Laughlin states on the sphere as representations of Uq(sl(2))

Cited by in corpus (4)

• Coulomb gas representation of quantum Hall effect on Riemann surfaces
• Laughlin states on the Poincare half-plane and its quantum group symmetry
• Quantum Hall Effect Wave Functions as Cyclic Representations of U_q(sl(2))
• An appropriate candidate for exact distribution of closed random walks using quantum groups