Coadjoint orbits of reductive type of seaweed Lie algebras

Anne Moreau (1) , Oksana Yakimova (2)

1 LMA [Poitiers] - Laboratoire de mathématiques et applications [UMR 6086]
2 Department Mathematik [Erlangen]

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.

Mots clés: Quasi-reductive Lie algebras; Lie algebras of seaweed type; Regular linear forms; Stabilisers.; Stabilisers

Domaines: Théorie des représentations [math.RT]

Anne Moreau, Oksana Yakimova. Coadjoint orbits of reductive type of seaweed Lie algebras. International Mathematics Research Notices, 2011, 45 p. ⟨10.1093/imrn/rnr184⟩. ⟨hal-00551382v2⟩