Composantes irréductibles de la variété commutante nilpotente d'une algèbre de Lie symétrique semi-simple

Details Composantes irréductibles de la variété commutante nilpotente d'une algèbre de Lie symétrique semi-simple Composantes irréductibles de la variété commutante nilpotente d'une algèbre de Lie symétrique semi-simple

2007-10-24

arxiv.org/abs/0710.4464v4

M. Bulois, Annales de l'Institut Fourier 59 (2009), 37-80

Mathematics

Representation Theory

38 pages, in french, minor changes, Journal-ref added

Scientific paper

Let \theta be an involution of the semisimple Lie algebra g and g=k+p be the associated Cartan decomposition. The nilpotent commuting variety of (g,\theta) consists in pairs of nilpotent elements (x,y) of p such that [x,y]=0. It is conjectured that this variety is equidimensional and that its irreducible components are indexed by the orbits of p-distinguished elements. This conjecture was established by A. Premet in the case (g \times g, \theta) where \theta(x,y)=(y,x). In this work we prove the conjecture in a significant number of other cases.

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