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Fixed point spaces in primitive actions of simple algebraic groups

Fixed point spaces in primitive actions of simple algebraic groups
Fixed point spaces in primitive actions of simple algebraic groups
Let G be a simple algebraic group of adjoint type acting primitively on an algebraic variety ?. We study the dimensions of the subvarieties of fixed points of involutions in G. In particular, we obtain a close to best possible function f(h), where h is the Coxeter number of G, with the property that with the exception of a small finite number of cases, there exists an involution t in G such that the dimension of the fixed point space of t is at least f(h)dim?.
0021-8693
744-771
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6
Burness, Timothy C.
a3b369f0-16f5-41e6-84d9-5a50f027bcd6

Burness, Timothy C. (2003) Fixed point spaces in primitive actions of simple algebraic groups. Journal of Algebra, 265 (2), 744-771. (doi:10.1016/S0021-8693(03)00270-9).

Record type: Article

Abstract

Let G be a simple algebraic group of adjoint type acting primitively on an algebraic variety ?. We study the dimensions of the subvarieties of fixed points of involutions in G. In particular, we obtain a close to best possible function f(h), where h is the Coxeter number of G, with the property that with the exception of a small finite number of cases, there exists an involution t in G such that the dimension of the fixed point space of t is at least f(h)dim?.

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Published date: 15 July 2003

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Local EPrints ID: 46628
URI: http://eprints.soton.ac.uk/id/eprint/46628
ISSN: 0021-8693
PURE UUID: e009f0a5-6977-4d93-be0c-be97a3298e79

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Date deposited: 09 Jul 2007
Last modified: 08 Jan 2022 03:56

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Author: Timothy C. Burness

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