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Regular version of the site

Article

Algebra and quantum geometry of multifrequency resonance

Izvestiya. Mathematics. 2010. Vol. 74. No. 6. P. 1155-1204.

The algebra of symmetries of a quantum resonance oscillator in the case of three and more frequencies is described using a finite (minimal) basis of generators and polynomial relations. For this algebra, we construct quantum leaves with complex structure (an analog of classical symplectic leaves) and a quantum K¨ahlerian 2-form, a reproducing measure, as well as the corresponding irreducible representations and coherent states.