Memoirs of the American Mathematical Society 2011; 188 pp; softcover Volume: 210 ISBN10: 0821847694 ISBN13: 9780821847695 List Price: US$88 Individual Members: US$52.80 Institutional Members: US$70.40 Order Code: MEMO/210/988
 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
