This article is cited in 4 papers

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.

UDC: 512.66

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

Received: 14.11.1981 and 08.09.1983

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

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