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Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups
R. Lawther, Girton College, University of Cambridge, England, and D. M. Testerman, École Polytechnique Federale de Lausanne, Switzerland
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Memoirs of the American Mathematical Society
188 pp; softcover
Volume: 210
ISBN-10: 0-8218-4769-4
ISBN-13: 978-0-8218-4769-5
List Price: US$83
Individual Members: US$49.80
Institutional Members: US$66.40
Order Code: MEMO/210/988
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Let \(G\) be a simple algebraic group defined over an algebraically closed field \(k\) whose characteristic is either \(0\) or a good prime for \(G\), and let \(u\in G\) be unipotent. The authors study the centralizer \(C_G(u)\), especially its centre \(Z(C_G(u))\). They calculate the Lie algebra of \(Z(C_G(u))\), in particular determining its dimension; they prove a succession of theorems of increasing generality, the last of which provides a formula for \(\dim Z(C_G(u))\) in terms of the labelled diagram associated to the conjugacy class containing \(u\).

Table of Contents

  • Introduction
  • Notation and preliminary results
  • Reduction of the problem
  • Classical groups
  • Exceptional groups: Nilpotent orbit representatives
  • Associated cocharacters
  • The connected centralizer
  • A composition series for the Lie algebra centralizer
  • The Lie algebra of the centre of the centralizer
  • Proofs of the main theorems for exceptional groups
  • Detailed results
  • Bibliography
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