New flag-transitive geometries for the groups Sp4(K) and SU5(K)

Justin F McInroy; Harm Pralle; Sergey Shpectorov

doi:10.1007/s10711-013-9928-0

New flag-transitive geometries for the groups Sp₄(K) and SU₅(K)

Justin F McInroy
, Harm Pralle
, Sergey Shpectorov

Research output: Contribution to journal › Article (Academic Journal) › peer-review

Abstract

In Pralle and Shpectorov (Adv Geom 7(1):1–17, 2007) the class of ovoidal hyperplanes in dual polar spaces of rank 4 is described. In this paper we observe that by removing such a hyperplane and a related second hyperplane one obtains a nice geometry for the group stabilising the ovoidal hyperplane. We show that this group acts flag-transitively and that the geometry is simply connected.

Original language	English
Pages (from-to)	65-82
Number of pages	18
Journal	Geometriae Dedicata
Volume	173
Issue number	1
Early online date	25 Oct 2013
DOIs	https://doi.org/10.1007/s10711-013-9928-0
Publication status	Published - 2014

Keywords

GEOMETRY
Polar space
HYPERPLANES
ovoidal hyperplane
flag-transitive
affine
Biaffine

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10.1007/s10711-013-9928-0

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Cite this

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title = "New flag-transitive geometries for the groups Sp4(K) and SU5(K)",

abstract = "In Pralle and Shpectorov (Adv Geom 7(1):1{\textendash}17, 2007) the class of ovoidal hyperplanes in dual polar spaces of rank 4 is described. In this paper we observe that by removing such a hyperplane and a related second hyperplane one obtains a nice geometry for the group stabilising the ovoidal hyperplane. We show that this group acts flag-transitively and that the geometry is simply connected.",

keywords = "GEOMETRY, Polar space, HYPERPLANES, ovoidal hyperplane, flag-transitive, affine, Biaffine",

author = "McInroy, \{Justin F\} and Harm Pralle and Sergey Shpectorov",

year = "2014",

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pages = "65--82",

journal = "Geometriae Dedicata",

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T1 - New flag-transitive geometries for the groups Sp4(K) and SU5(K)

AU - McInroy, Justin F

AU - Pralle, Harm

AU - Shpectorov, Sergey

PY - 2014

Y1 - 2014

N2 - In Pralle and Shpectorov (Adv Geom 7(1):1–17, 2007) the class of ovoidal hyperplanes in dual polar spaces of rank 4 is described. In this paper we observe that by removing such a hyperplane and a related second hyperplane one obtains a nice geometry for the group stabilising the ovoidal hyperplane. We show that this group acts flag-transitively and that the geometry is simply connected.

AB - In Pralle and Shpectorov (Adv Geom 7(1):1–17, 2007) the class of ovoidal hyperplanes in dual polar spaces of rank 4 is described. In this paper we observe that by removing such a hyperplane and a related second hyperplane one obtains a nice geometry for the group stabilising the ovoidal hyperplane. We show that this group acts flag-transitively and that the geometry is simply connected.

KW - GEOMETRY

KW - Polar space

KW - HYPERPLANES

KW - ovoidal hyperplane

KW - flag-transitive

KW - affine

KW - Biaffine

U2 - 10.1007/s10711-013-9928-0

DO - 10.1007/s10711-013-9928-0

M3 - Article (Academic Journal)

SN - 0046-5755

VL - 173

SP - 65

EP - 82

JO - Geometriae Dedicata

JF - Geometriae Dedicata

IS - 1

ER -