Coadjoint orbits of reductive type of seaweed Lie algebras
Abstract
A connected algebraic group Q defined over a field of characteristic zero is quasi-reductive if there is an element of its dual of reductive type, that is such that the quotient of its stabiliser by the centre of Q is a reductive subgroup of GL(q), where q=Lie(Q). Due to results of M. Duflo, coadjoint representation of a quasi-reductive Q possesses a so called maximal reductive stabiliser and knowing this subgroup, defined up to a conjugation in Q, one can describe all coadjoint orbits of reductive type. In this paper, we consider quasi-reductive parabolic subalgebras of simple complex Lie algebras as well as all seaweed subalgebras of gl(n) and describe the classes of their maximal reductive stabilisers.
Keywords
Cite
@article{arxiv.1101.0902,
title = {Coadjoint orbits of reductive type of seaweed Lie algebras},
author = {Anne Moreau and Oksana Yakimova},
journal= {arXiv preprint arXiv:1101.0902},
year = {2011}
}
Comments
35 pages, 5 figures; International Mathematics Research Notices (2011) 45 pages