Harmonic analysis on Lagrangian manifolds of integrable Hamiltonian systems

Abstract

For an integrable Hamiltonian system we construct a representation of the phase space symmetry algebra over the space of functions on a Lagrangian manifold. The representation is a result of the canonical quantization of the integrable system in terms of separation variables. The variables are chosen in such way that a half of them parameterizes the Lagrangian manifold, which coincides with the Liouville torus of the integrable system. The obtained representation is indecomposable and non-exponentiated.

13 pages, XIVth International Conference 'Geometry, Integrability and Quantization', June 8-13, 2012, Varna, Bulgaria