Sheets of symmetric Lie algebras and slice induction

Michael Bulois (1) , Pascal Hivert (2)

1 AGL - Algèbre, géométrie, logique
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 desingularization lying in so7.In this new version, computations of section 4 are pared down. Important modifications of the exposition of Section 3 on slice induction.

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

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

Michael Bulois, Pascal Hivert. Sheets of symmetric Lie algebras and slice induction. Transformation Groups, 2016, 21 (2), pp.355-375. ⟨10.1007/s00031-015-9355-4⟩. ⟨hal-01017691v3⟩