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On Extensions of Canonical Symplectic Structure from Coadjoint Orbit of Complex General Linear Group

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The problem of extensions of the canonical Lee–Poisson–Kirillov–Kostant symplectic structure of coadjoint orbit of the complex general linear group is considered. The introduced method uses the concept of flag coordinates and does not depend on the Jordan structure of the matrices that form the orbit. The principal bundle associated with the fibration of the orbit over the Grassmanian of flags is constructed.

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Authors and Affiliations

  1. St.Petersburg Department of the Steklov Mathematical Institute, St.Petersburg State University, St.Petersburg, Russia

    M. V. Babich

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  1. M. V. Babich
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Correspondence to M. V. Babich.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 487, 2019, pp. 28–39.

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Babich, M.V. On Extensions of Canonical Symplectic Structure from Coadjoint Orbit of Complex General Linear Group. J Math Sci 257, 442–449 (2021). https://doi.org/10.1007/s10958-021-05502-3

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  • DOI: https://doi.org/10.1007/s10958-021-05502-3

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