Sheets, slice induction and G2(2) case

Michael Bulois (1) , Pascal Hivert (2)

1 ICJ - Institut Camille Jordan
2 algèbre et géométrie

In this paper, we study sheets of symmetric Lie algebras through their Slodowy slices. In particular, we introduce a notion of slice induction of nilpotent orbits which coincides with the parabolic induction in the Lie algebra case. We also study in more details the sheets of the non-trivial symmetric Lie algebra of type G2. We characterize their singular loci and provide a nice desingularisation lying in so7.

Mots clés: sheets; induction; Lie algebras; symmetric Lie algebra; Jordan classes

Domaines: Théorie des représentations [math.RT]; Géométrie algébrique [math.AG]

Michael Bulois, Pascal Hivert. Sheets, slice induction and G2(2) case. 2014. ⟨hal-01017691v2⟩