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Polar spaces and embeddings of classical groups

Gill, Nick (2007). Polar spaces and embeddings of classical groups. New Zealand Journal of Mathematics, 36 pp. 175–184.

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Abstract

Given polar spaces (V,β) and (V,Q) where V is a vector space over a field K, β a reflexive sesquilinear form and Q a quadratic form, we have associated classical isometry groups. Given a subfield F of K and an F-linear function L : KF we can define new spaces (V,Lβ) and (V,LQ) which are polar spaces over F.
The construction so described gives an embedding of the isometry groups of (V,β) and (V,Q) into the isometry groups of (V,Lβ) and (V,LQ).In the finite field case under certain added restrictions these subgroups are maximal and form the so called field extension subgroups of Aschbacher's class C3.
We give precise descriptions of the polar spaces so defined and their associated isometry group embeddings. In the finite field case our results give extra detail to the account of maximal field extension subgroups given by Kleidman and Liebeck.

Item Type: Journal Article
Copyright Holders: 2007 The Author
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 28190
Depositing User: Nick Gill
Date Deposited: 17 Feb 2011 12:08
Last Modified: 18 Feb 2011 05:44
URI: http://oro.open.ac.uk/id/eprint/28190
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