On the centralizer of a balanced nilpotent section

2018/10/15 by William Hardesty, Hardesty, William
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1810.06157

openalex publication_date 2018/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a split reductive algebraic group defined over a complete discrete valuation ring \mathbbO, with residue field \mathbbF and fraction field \mathbbK, where the fiber G_\mathbbF is geometrically standard. A balanced nilpotent section x ∈ Lie(G) can roughly be thought of as an \mathbbO-point in a \mathbbK nilpotent orbit such that the corresponding orbits over \mathbbK and \mathbbF have the same Bala--Carter label. In this paper, we will establish a number of results on the structure of the centralizer G^x ⊆ G of x. This includes a proof that G^x is a smooth group scheme, and that the component groups of its geometric fibers are isomorphic.

Citations

• Nilpotent orbits over ground fields of good characteristic
• Component groups of unipotent centralizers in good characteristic

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• Nilpotent orbits over ground fields of good characteristic
• Orbit closures in flag varieties for the centralizer of an order-two nilpotent element : normality and resolutions for types A, B, D
• Nilpotent centralizers and Springer isomorphisms
• Centralizers of sections of a reductive group scheme