Nagoya Mathematical Journal

On cocharacters associated to nilpotent elements of reductive groups

Russell Fowler and Gerhard Röhrle

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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.

Article information

Source
Nagoya Math. J., Volume 190 (2008), 105-128.

Dates
First available in Project Euclid: 23 June 2008

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1214229080

Mathematical Reviews number (MathSciNet)
MR2423831

Zentralblatt MATH identifier
1185.20050

Subjects
Primary: 20G15: Linear algebraic groups over arbitrary fields 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
Secondary: 17B50: Modular Lie (super)algebras

Keywords
Cocharacters associated to nilpotent elements

Citation

Fowler, Russell; Röhrle, Gerhard. On cocharacters associated to nilpotent elements of reductive groups. Nagoya Math. J. 190 (2008), 105--128. https://projecteuclid.org/euclid.nmj/1214229080


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