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

2009; Association of the Annals of the Fourier Institute; Volume: 59; Issue: 1 Linguagem: Inglês

10.5802/aif.2426

1777-5310

Michaël Bulois,

Algebraic structures and combinatorial models

Let θ be an involution of the finite dimensional semisimple Lie algebra 𝔤 and 𝔤=𝔨⊕𝔭 be the associated Cartan decomposition. The nilpotent commuting variety of (𝔤,θ) 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×𝔤,θ) where θ(x,y)=(y,x). In this work we prove the conjecture in a significant number of other cases.