eBook ISBN:  9781470406059 
Product Code:  MEMO/210/988.E 
List Price:  $88.00 
MAA Member Price:  $79.20 
AMS Member Price:  $52.80 
eBook ISBN:  9781470406059 
Product Code:  MEMO/210/988.E 
List Price:  $88.00 
MAA Member Price:  $79.20 
AMS Member Price:  $52.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 210; 2011; 188 ppMSC: Primary 20
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

1. Introduction

2. Notation and preliminary results

3. Reduction of the problem

4. Classical groups

5. Exceptional groups: Nilpotent orbit representatives

6. Associated cocharacters

7. The connected centralizer

8. A composition series for the Lie algebra centralizer

9. The Lie algebra of the centre of the centralizer

10. Proofs of the main theorems for exceptional groups

11. Detailed results

References


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
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 \(u\).

1. Introduction

2. Notation and preliminary results

3. Reduction of the problem

4. Classical groups

5. Exceptional groups: Nilpotent orbit representatives

6. Associated cocharacters

7. The connected centralizer

8. A composition series for the Lie algebra centralizer

9. The Lie algebra of the centre of the centralizer

10. Proofs of the main theorems for exceptional groups

11. Detailed results

References