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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

Memoirs of the American Mathematical Society
2011; 188 pp; softcover
Volume: 210
ISBN-10: 0-8218-4769-4
ISBN-13: 978-0-8218-4769-5
List Price: US$88
Individual Members: US$52.80
Institutional Members: US$70.40
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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