# An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras

Dmitri I. Panyushev^{[1]}

- [1] Independent university of Moscow, Bol'shoi Vlaservskii per.11, 119002 Moscow (Russia)

Annales de l’institut Fourier (2005)

- Volume: 55, Issue: 3, page 693-715
- ISSN: 0373-0956

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topI. Panyushev, Dmitri. "An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras." Annales de l’institut Fourier 55.3 (2005): 693-715. <http://eudml.org/doc/116204>.

@article{I2005,

abstract = {We prove an extension of Rais' theorem on the coadjoint representation of certain graded
Lie algebras. As an application, we prove that, for the coadjoint representation of any
seaweed subalgebra in a general linear or symplectic Lie algebra, there is a generic
stabiliser and the field of invariants is rational. It is also shown that if the highest
root of a simple Lie algerba is not fundamental, then there is a parabolic subalgebra
whose coadjoint representation do not have a generic stabiliser.},

affiliation = {Independent university of Moscow, Bol'shoi Vlaservskii per.11, 119002 Moscow (Russia)},

author = {I. Panyushev, Dmitri},

journal = {Annales de l’institut Fourier},

keywords = {field of invariants; generic stabiliser; simple Lie algebra; seaweed subalgebra},

language = {eng},

number = {3},

pages = {693-715},

publisher = {Association des Annales de l'Institut Fourier},

title = {An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras},

url = {http://eudml.org/doc/116204},

volume = {55},

year = {2005},

}

TY - JOUR

AU - I. Panyushev, Dmitri

TI - An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras

JO - Annales de l’institut Fourier

PY - 2005

PB - Association des Annales de l'Institut Fourier

VL - 55

IS - 3

SP - 693

EP - 715

AB - We prove an extension of Rais' theorem on the coadjoint representation of certain graded
Lie algebras. As an application, we prove that, for the coadjoint representation of any
seaweed subalgebra in a general linear or symplectic Lie algebra, there is a generic
stabiliser and the field of invariants is rational. It is also shown that if the highest
root of a simple Lie algerba is not fundamental, then there is a parabolic subalgebra
whose coadjoint representation do not have a generic stabiliser.

LA - eng

KW - field of invariants; generic stabiliser; simple Lie algebra; seaweed subalgebra

UR - http://eudml.org/doc/116204

ER -

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