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 Mat. Zametki, 2018, Volume 104, Issue 6, paper published in the English version journal (Mi mz12344)

Papers published in the English version of the journal

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

M. V. Karasev, E. M. Novikova

National Research University Higher School of Economics, Moscow, 101000 Russia

Abstract: 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.

Keywords: frequency resonance, algebra of symmetries, nonlinear commutation relations, coherent states.

 Funding Agency Grant Number National Research University Higher School of Economics This work was supported by the Program for Fundamental Research of the National Research University Higher School of Economics.

English version:
Mathematical Notes, 2018, 104:6, 833–847

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Citation: M. V. Karasev, E. M. Novikova, “Algebra of Symmetries of Three-Frequency Resonance: Reduction of a Reducible Case to an Irreducible Case”, Math. Notes, 104:6 (2018), 833–847

Citation in format AMSBIB
\Bibitem{KarNov18} \by M.~V.~Karasev, E.~M.~Novikova \paper Algebra of Symmetries of Three-Frequency Resonance: Reduction of a Reducible Case to an Irreducible Case \jour Math. Notes \yr 2018 \vol 104 \issue 6 \pages 833--847 \mathnet{http://mi.mathnet.ru/mz12344} \crossref{https://doi.org/10.1134/S0001434618110287} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000454546800028} \elib{http://elibrary.ru/item.asp?id=38655639} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85059282219}