On cocharacters associated to nilpotent elements of reductive groups

Details On cocharacters associated to nilpotent elements of reductive groups On cocharacters associated to nilpotent elements of reductive groups

2006-08-08

arxiv.org/abs/math/0608194v3

Mathematics

Representation Theory

16 pages, to appear in Nagoya Math. J

Scientific paper

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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