Geodesic
The symplectic structure of the orbits of the coadjoint representation of Lie algebras of type $E\underset{\rho}\times G$
Sbornik. Mathematics, Tome 51 (1985) no. 1, pp. 275-286 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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T. A. Pevtsova. The symplectic structure of the orbits of the coadjoint representation of Lie algebras of type $E\underset{\rho}\times G$. Sbornik. Mathematics, Tome 51 (1985) no. 1, pp. 275-286. http://geodesic.mathdoc.fr/item/SM_1985_51_1_a17/

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