Sheets, slice induction and G2(2) case

2014/07/03 by Michael Bulois, Michaël Bulois, Bulois, Michael +2
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.1407.1010

22 pages. In this new version, computations of section 4 are pared down. Important modifications of the exposition of Section 3 on slice induction

arxiv created 2015/02/26 · arxiv updated 2015/02/27

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.

Related

• A new construction of D₅-singularities and generalization of Slodowy slices
• Equivariant deformation theory for nilpotent slices in symplectic Lie algebras
• Generalized Amitsur-Levitski theorem and equations for sheets in a reductive complex Lie algebra
• Rigid 2-step graph Lie algebras
• The structure of the nilpotent cone, the Kazhdan-Lusztig map and algebraic group analogues of the Slodowy slices