Vol. 104, No. 1, 1983

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Centralizers of irregular elements in reductive algebraic groups

John Francis Kurtzke, Jr.

Vol. 104 (1983), No. 1, 133–154
Abstract

Let G be a reductive linear algebraic group defined over an algebraically closed field K. An element x G is called regular if dimZG(x) is the rank of G—which is the smallest possible dimension for a centralizer—otherwise x is called irregular. T. A. Springer has shown that if x G is regular, then ZG(x)0 is abelian. In this paper, we show that when char K is good for G, the converse is also true—if x G is irregular, then ZG(x)0 is nonabelian. In the course of the proof of this, we show that if G is a classical group or G2 (char K good), then dimZ(ZG(x)0) is at most rank G. Further, if G = Sp2n(K)(char K2), then Z(ZG(x)0) consists of polynomials in x.

Mathematical Subject Classification 2000
Primary: 20G15
Secondary: 14L10
Milestones
Received: 25 January 1980
Revised: 30 November 1981
Published: 1 January 1983
Authors
John Francis Kurtzke, Jr.