Mathematical Notes

, Volume 104, Issue 5–6, pp 833–847 | Cite as

Algebra of Symmetries of Three-Frequency Resonance: Reduction of a Reducible Case to an Irreducible Case

  • M. V. KarasevEmail author
  • E. M. Novikova


For the three-frequency quantum resonance oscillator, the reducible case, where the frequencies are integer and at least one pair of frequencies has a nontrivial common divisor, is studied. It is shown how the description of the algebra of symmetries of such an oscillator can be reduced to the irreducible case of pairwise coprime integer frequencies. Polynomial algebraic relations are written, and irreducible representations and coherent states are constructed.


frequency resonance algebra of symmetries nonlinear commutation relations coherent states 


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia

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