2011/08/30 by Matthew C. Clarke, Clarke, Matthew C., Alexander Premet +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT
paper · pdf · doi:10.48550/arxiv.1108.5889
30 pages
openalex publication_date 2011/08/30 · arxiv created 2011/09/19 · arxiv updated 2011/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a connected reductive algebraic group over an algebraically closed field of characteristic p ≥ 0. We give a case-free proof of Lusztig's conjectures [Unipotent elements in small characteristic, \em Transform. Groups 10 (2005), 449--487] on so-called unipotent pieces. This presents a uniform picture of the unipotent elements of G which can be viewed as an extension of the Dynkin--Kostant theory, but is valid without restriction on p. We also obtain analogous results for the adjoint action of G on its Lie algebra \gl and the coadjoint action of G on \gl^*.