An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras
| dc.creator | Panyushev, Dmitri I. | |
| dc.date | 2004-09-03 | |
| dc.date.accessioned | 2026-07-07T05:11:47Z | |
| dc.date.available | 2026-07-07T05:11:47Z | |
| dc.description | Let $\g$ be a simple Lie algebra of type A or C. We show that the coadjoint representation of any seaweed subalgebra of $\g$ has some properties similar to that of the adjoint representation of a reductive Lie algebra. Namely, a) the field of invariants is rational and b) there exists a generic stabiliser whose identity component is a torus. Our main tool for this is a result about coadjoint representations of some N-graded Lie algebras, which can be regarded as an extension of Rais' theorem for the index of semi-direct products. For all other simple types, we give a uniform description of a parabolic subalgebra such that its coadjoint representation has no generic stabiliser. The crucial property here is that if $\g$ is not of type A or C, then the highest root is fundamental. We also show that, for any parabolic subgroup, the ring of regular invariants of the coadjoint representation is trivial. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409055 | |
| dc.identifier | http://arxiv.org/abs/math/0409055 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72362 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Representation Theory | |
| dc.title | An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras | |
| dc.type | text |