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Coadjoint orbits of reductive type

Giovedi 9 dicembre 2010 - Anne Moreau

ARGOMENTI: Seminari

Giovedi 9 dicembre 2010 alle ore 11.30 in Aula 1BC45 la Dott.ssa Anne Moreau (Poitiers) terra' una conferenza dal titolo "Coadjoint orbits of reductive type".

-Abstract
A connected Lie group Q over a field of characteristic zero is quasi-reductive if it has linear forms of reductive type, that is such that the quotient of its stabiliser by the center of Q is a reductive subgroup of GL(q) where q = Lie(Q). In the real case, such Lie groups have irreducible unitary square integrable representations. By Duflo's work, the description of their maximal reductive stabilizers enables to parameterize these representations.
The classification of quasi-reductive parabolic subalgebras of simple complex Lie algebras have been recently achieved, by Panyushev and Duflo for the classical cases, and by K. Baur and myself for the exceptional cases. More recently, in a joint work with O. Yakimova, we describe, for each of these quasi-reductive Lie algebras, their maximal reductive stabilizers. In this talk, I will present these two works.

Rif. int. G. Carnovale