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Algebra i Analiz, 2010, Volume 22, Issue 3, Pages 16–31 (Mi aa1184)  

This article is cited in 11 scientific papers (total in 11 papers)

Research Papers

On rational symplectic parametrization of the coadjoint orbit of GL(N)GL(N). Diagonalizable case

M. V. Babich, S. E. Derkachov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
References:
Abstract: A method for constructing birational Darboux coordinates on a coadjoint orbit of the general linear group is presented. This method is based on the Gauss decomposition of a matrix in the product of an upper-triangular and a lower-triangular matrix. The method works uniformly for the orbits formed by the diagonalizable matrices of any size and for arbitrary dimensions of the eigenspaces.
Keywords: Darboux coordinates, symplectic form, Poisson bracket, coadjoint orbit.
Received: 15.02.2010
English version:
St. Petersburg Mathematical Journal, 2011, Volume 22, Issue 3, Pages 347–357
DOI: https://doi.org/10.1090/S1061-0022-2011-01145-8
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. V. Babich, S. E. Derkachov, “On rational symplectic parametrization of the coadjoint orbit of GL(N)GL(N). Diagonalizable case”, Algebra i Analiz, 22:3 (2010), 16–31; St. Petersburg Math. J., 22:3 (2011), 347–357
Citation in format AMSBIB
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\pages 347--357
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Linking options:
  • https://www.mathnet.ru/eng/aa1184
  • https://www.mathnet.ru/eng/aa/v22/i3/p16
  • This publication is cited in the following 11 articles:
    1. Ilia Gaiur, Marta Mazzocco, Vladimir Rubtsov, “Isomonodromic Deformations: Confluence, Reduction and Quantisation”, Commun. Math. Phys., 400:2 (2023), 1385  crossref
    2. N. Belousov, S. Derkachov, “Regular Representation of the Group GL(N, ℝ): Factorization, Casimir Operators and Toda Chain”, J Math Sci, 264:3 (2022), 215  crossref
    3. N. M. Belousov, S. E. Derkachev, “Regulyarnoe predstavlenie gruppy GL(N,R): faktorizatsiya, operatory Kazimira i tsepochka Tody”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 27, Zap. nauchn. sem. POMI, 494, POMI, SPb., 2020, 23–47  mathnet
    4. Babich V M., “On Canonical Parametrization of Phase Spaces of Isomonodromic Deformation Equations”, Geometric Methods in Physics Xxxvii, Trends in Mathematics, eds. Kielanowski P., Odzijewicz A., Previato E., Birkhauser Verlag Ag, 2020, 3–12  mathscinet  isi
    5. M. V. Babich, “On extensions of canonical symplectic structure from coadjoint orbit of complex general linear group”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 26, Zap. nauchn. sem. POMI, 487, POMI, SPb., 2019, 28–39  mathnet
    6. J. Math. Sci. (N. Y.), 242:5 (2019), 587–594  mathnet  crossref
    7. J. Math. Sci. (N. Y.), 238:6 (2019), 763–768  mathnet  crossref
    8. M. V. Babich, “Birational Darboux Coordinates on (Co)Adjoint Orbits of GL(N,C)”, Funct. Anal. Appl., 50:1 (2016), 17–30  mathnet  crossref  crossref  mathscinet  isi  elib
    9. J. Math. Sci. (N. Y.), 209:6 (2015), 830–844  mathnet  crossref
    10. M. V. Babich, “Young tableaux and stratification of space of complex square matrices”, J. Math. Sci. (N. Y.), 213:5 (2016), 651–661  mathnet  crossref  mathscinet
    11. Babich M.V., “On birational Darboux coordinates of isomonodromic deformation equations phase space”, Painleve Equations and Related Topics (St. Petersburg, June 17–23, 2011), DeGruyter Proceedings in Mathematics, eds. Bruno A., Batkhin A., Walter de Gruyter & Co, 2012, 91–94  mathscinet  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    Алгебра и анализ St. Petersburg Mathematical Journal
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