On cocharacters associated to nilpotent elements of reductive groups

2006/08/08 by Russell Fowler, Gerhard Roehrle, Fowler, Russell +1
Chemistry · Mathematics · #14L30 #20G15 #Advanced Algebra and Geometry #Crystal structures of chemical compounds #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.math/0608194

openalex publication_date 2006/08/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a connected reductive linear algebraic group defined over an algebraically closed field of characteristic p. Assume that p is good for G. In this note we consider particular classes of connected reductive subgroups H of G and show that the cocharacters of H that are associated to a given nilpotent element e in the Lie algebra of H are precisely the cocharacters of G associated to e that take values in H. In particular, we show that this is the case provided H is a connected reductive subgroup of G of maximal rank; this answers a question posed by J.C. Jantzen.

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