Sheets, slice induction and G2(2) case

Abstract

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.