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 Mat. Sb. (N.S.), 1984, Volume 123(165), Number 2, Pages 276–286 (Mi msb2005)

The symplectic structure of the orbits of the coadjoint representation of Lie algebras of type $E\underset{\rho}\times G$

T. A. Pevtsova

Abstract: The following theorem is proved.
Theorem. Let $G$ be the semidirect sum of a simple Lie algebra $H$ and an Abelian algebra relative to representation $\mu$. Then a complete involutive system of rational functions on $G^*$ is explicitly constructed in the following cases: a) {\it$H=\operatorname{gl}(2n)$ and $\mu=\Lambda^2\rho$;} b) {\it$H=\operatorname{sl}(2n)$ and $\mu=s^2\rho$;} c) {\it$H=\operatorname{sp}(2n)$ and $\mu=\rho+\tau$, where $\rho$ is the minimal representation and $\tau$ is the one-dimensional trivial representation.}
Bibliography: 9 titles.

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English version:
Mathematics of the USSR-Sbornik, 1985, 51:1, 275–286

Bibliographic databases:

UDC: 512.66
MSC: Primary 17B15, 58F05; Secondary 22E30

Citation: T. A. Pevtsova, “The symplectic structure of the orbits of the coadjoint representation of Lie algebras of type $E\underset{\rho}\times G$”, Mat. Sb. (N.S.), 123(165):2 (1984), 276–286; Math. USSR-Sb., 51:1 (1985), 275–286

Citation in format AMSBIB
\Bibitem{Pev84} \by T.~A.~Pevtsova \paper The symplectic structure of the orbits of the coadjoint representation of Lie algebras of type $E\underset{\rho}\times G$ \jour Mat. Sb. (N.S.) \yr 1984 \vol 123(165) \issue 2 \pages 276--286 \mathnet{http://mi.mathnet.ru/msb2005} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=732391} \zmath{https://zbmath.org/?q=an:0538.58013|0569.58011} \transl \jour Math. USSR-Sb. \yr 1985 \vol 51 \issue 1 \pages 275--286 \crossref{https://doi.org/10.1070/SM1985v051n01ABEH002860} 

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This publication is cited in the following articles:
1. A. V. Bolsinov, “Involutory families of functions on dual spaces of Lie algebras of type $G\underset\varphi+ V$”, Russian Math. Surveys, 42:6 (1987), 227–228
2. A. V. Bolsinov, “Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution”, Math. USSR-Izv., 38:1 (1992), 69–90
3. M. M. Zhdanova, “Completely integrable Hamiltonian systems on semidirect sums of Lie algebras”, Sb. Math., 200:5 (2009), 629–659
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