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SUMMARY:Triality\, two geometries and one amalgam non-uniqueness result - 
 Dr. Justin McInroy (Lincoln College\, Oxford)
DTSTART:20111104T140000Z
DTEND:20111104T150000Z
UID:TALK34116@talks.cam.ac.uk
CONTACT:Joanna Fawcett
DESCRIPTION:A polar space $\\Pi$ is a geometry whose elements are the tota
 lly isotropic subspaces of a vector space $V$ with respect to either an al
 ternating\, Hermitian\, or quadratic form. We may form a new geometry $\\G
 amma$ by removing all elements contained in either a hyperplane $F$ of $\\
 Pi$\, or a hyperplane $H$ of the dual $\\Pi^*$. This is a \\emph{biaffine 
 polar space}.\n\nWe will discuss two specific examples arising from the tr
 iality in $O^+_8(q)$.  By considering the stabilisers of a maximal flag\, 
 we get an amalgam\, or "glueing"\, of groups for each example. However\, t
 he two examples have "similar" amalgams - this leads to a group recognitio
 n result for their automorphism groups\, $q^7:G_2(q)$ and $Spin_7(q)$.
LOCATION:MR4
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