Area-preserving diffeomorphisms, W∞ and $Uq(sl(2)) in Chern-Simons theory and Quantum Hall system
Ian I. Kogan
Abstract
We discuss a quantum symmetry in Landau problem, which naturally arises due to the relation between the and the group of magnetic translations. The last one is connected with the and area-preserving (symplectic) diffeomorphisms which are the canonical transformations in the two-dimenssional phase space. We shall discuss the hidden quantum symmetry in a 2+1 gauge theory with the Chern-Simons term and in aQuantum Hall system which are both connected with the Landau problem.
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