M. V. Babich, S. E. Derkachov, “On rational symplectic parametrization of the coadjoint orbit of $\mathrm{GL}(N)$. Diagonalizable case”, Algebra i Analiz, 22:3 (2010), 16–31; St. Petersburg Math. J., 22:3 (2011), 347

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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

$\mathrm{GL}(N)$ . 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

Full-text PDF (636 kB) Citations (11)

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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

$\mathrm{GL}(N)$ . 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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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:

Ilia Gaiur, Marta Mazzocco, Vladimir Rubtsov, “Isomonodromic Deformations: Confluence, Reduction and Quantisation”, Commun. Math. Phys., 400:2 (2023), 1385
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
N. M. Belousov, S. E. Derkachev, “Regulyarnoe predstavlenie gruppy $\mathrm{GL}(N,\mathbb{R})$: faktorizatsiya, operatory Kazimira i tsepochka Tody”, Voprosy kvantovoi teorii polya i statisticheskoi fiziki. 27, Zap. nauchn. sem. POMI, 494, POMI, SPb., 2020, 23–47
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
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
J. Math. Sci. (N. Y.), 242:5 (2019), 587–594
J. Math. Sci. (N. Y.), 238:6 (2019), 763–768
M. V. Babich, “Birational Darboux Coordinates on (Co)Adjoint Orbits of $\operatorname{GL}(N,\mathbb C)$”, Funct. Anal. Appl., 50:1 (2016), 17–30
J. Math. Sci. (N. Y.), 209:6 (2015), 830–844
M. V. Babich, “Young tableaux and stratification of space of complex square matrices”, J. Math. Sci. (N. Y.), 213:5 (2016), 651–661
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

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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