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Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups
 
R. Lawther :  Girton College, University of Cambridge, Cambridge, England
D. M. Testerman :  École Polytechnique Federale de Lausanne, Lausanne, Switzerland
Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups
eBook ISBN:  978-1-4704-0605-9
Product Code:  MEMO/210/988.E
List Price: $88.00
MAA Member Price: $79.20
AMS Member Price: $52.80
Add to cart
Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups
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Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups
R. Lawther :  Girton College, University of Cambridge, Cambridge, England
D. M. Testerman :  École Polytechnique Federale de Lausanne, Lausanne, Switzerland
eBook ISBN:  978-1-4704-0605-9
Product Code:  MEMO/210/988.E
List Price: $88.00
MAA Member Price: $79.20
AMS Member Price: $52.80
Add to cart
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 210; 2011; 188 pp
    MSC: 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Memoirs of the American Mathematical Society
Volume: 210; 2011; 188 pp
MSC: 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 \(u\).
  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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