Geometric quantization of the Landau problem on hyperbolic Riemann Surfaces

Antonio Lopez Almorox, Carlos Tejero Prieto


Abstract. The techniques of symplectic reduction are applied to the study of the Landau problem on the Poincar\'e plane and compact Riemann surfaces of genus $g>1$. This allows us to study the manifold of orbits of constant energy. Once this is done we proceed to study the geometric quantization of this problem showing its relationship, in the compact case, with Maass automorphic forms and operators.

AMSclassification. 58F05, 58F06, 81S10, 11F03,11F37

Keywords. Geometric quantization, Landau problem, Negative curvature, Automorphic forms