**Memoirs of the American Mathematical Society**

2011;
188 pp;
Softcover

MSC: Primary 20;

Print ISBN: 978-0-8218-4769-5

Product Code: MEMO/210/988

List Price: $88.00

AMS Member Price: $52.80

MAA Member Price: $79.20

**Electronic ISBN: 978-1-4704-0605-9
Product Code: MEMO/210/988.E**

List Price: $88.00

AMS Member Price: $52.80

MAA Member Price: $79.20

# Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

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*R. Lawther; D. M. Testerman*

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

# Table of Contents

## Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

- 1. Introduction 18 free
- 2. Notation and preliminary results 512 free
- 3. Reduction of the problem 1017
- 4. Classical groups 1421
- 5. Exceptional groups: Nilpotent orbit representatives 2229
- 6. Associated cocharacters 3340
- 7. The connected centralizer 3542
- 8. A composition series for the Lie algebra centralizer 4249
- 9. The Lie algebra of the centre of the centralizer 4855
- 10. Proofs of the main theorems for exceptional groups 6572
- 11. Detailed results 7178
- References 187194