|
This article is cited in 3 scientific papers (total in 3 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.
Received: 14.11.1981 and 08.09.1983
Citation:
T. A. Pevtsova, “The symplectic structure of the orbits of the coadjoint representation of Lie algebras of type $E\underset{\rho}\times G$”, Math. USSR-Sb., 51:1 (1985), 275–286
Linking options:
https://www.mathnet.ru/eng/sm2005https://doi.org/10.1070/SM1985v051n01ABEH002860 https://www.mathnet.ru/eng/sm/v165/i2/p276
|
Statistics & downloads: |
Abstract page: | 394 | Russian version PDF: | 93 | English version PDF: | 19 | References: | 61 |
|