Centres of centralizers of unipotent elements in simple algebraic groups / R. Lawther, D. M. Testerman.

Format:

Book

Author/Creator:

Lawther, R. (Ross), 1960- author.

Testerman, Donna M., 1960- author.

Series:

Memoirs of the American Mathematical Society ; Volume 210, Number 988.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 210, Number 988

Language:

English

Subjects (All):

Linear algebraic groups.

Physical Description:

1 online resource (188 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2010.

Language Note:

English

Summary:

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 uEG be unipotent. The authors study the centralizer CG(u) , especially its centre Z(CG(u)) . They calculate the Lie algebra of Z(CG(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(CG(u)) in terms of the labelled diagram associated to the conjugacy class containing u .

Contents:

""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""

Notes:

"Volume 210, Number 988 (first of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0605-5