Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups
- ISBN-10
- 0821847694
- ISBN-13
- 9780821847695
- Category
- Mathematics
- Pages
- 188
- Language
- English
- Published
- 2011
- Publisher
- American Mathematical Soc.
- Authors
- Donna M. Testerman, Ross Lawther
Description
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 $u$.
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