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On Cocharacters Associated to Nilpotent Elements of Reductive Groups

Published online by Cambridge University Press:  11 January 2016

Russell Fowler  and
Gerhard Röhrle
Russell Fowler
Affiliation:
School of Mathematics, University of Birmingham, Birmingham, B15 2TT, UK
Gerhard Röhrle
Affiliation:
Fakultät für Mathematik, Ruhr-Universität Bochum, D-44780 Bochum, Germany, gerhard.roehrle@rub.de
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Abstract

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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.

Keywords

20G1514L3017B50
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 190 , 2008 , pp. 105 - 128
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

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