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

Harmonic analysis on Lagrangian manifolds of integrable Hamiltonian systems