Location of Repository

Polar spaces and embeddings of classical groups

By Nick Gill

Abstract

Given polar spaces (<i>V</i>,β) and (<i>V,Q</i>) where <i>V</i> is a vector space over a field <i>K</i>, β a reflexive sesquilinear form and <i>Q</i> a quadratic form, we have associated classical isometry groups. Given a subfield <i>F</i> of <i>K</i> and an <i>F</i>-linear function <i>L</i> : <i>K</i> → <i>F</i> we can define new spaces (<i>V</i>,<i>L</i>β) and (<i>V</i>,<i>LQ</i>) which are polar spaces over <i>F</i>.<br></br>The construction so described gives an embedding of the isometry groups of (<i>V</i>,β) and (<i>V</i>,<i>Q</i>) into the isometry groups of (<i>V</i>,<i>L</i>β) and (<i>V</i>,<i>LQ</i>).In the finite field case under certain added restrictions these subgroups are maximal and form the so called <i>field extension subgroups</i> of Aschbacher's class <i>C</i><sub>3</sub>.<br></br>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

Year: 2007
OAI identifier: oai:oro.open.ac.uk:28190
Provided by: Open Research Online

Suggested articles

Preview


To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.