Intersection pattern of the classical ovoids in symplectic 3-space of even order
type: Item
instance of: scholarly article
title: Intersection pattern of the classical ovoids in symplectic 3-space of even order
zbMATH Open document ID: 0685.51006
DOI: 10.1016/0021-8693(89)90324-4
author: Bhaskar Bagchi
author: N. S. Narasimha Sastry
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: The authors prove several theorems on classical ovoids in symplectic 3- space \(W(s)\) for \(s=2^ e\), \(e>1\) odd. They determine how the copies of the Suzuki group \(Sz(s)\) in the symplectic group \(Sp(4,s)\) intersect and how the classical ovoids in symplectic 3-space \(W(s)\) meet and obtain a complete set of double coset representatives of \(Sz(s)\) in \(Sp(4,s)\). Towards the study of the permutation representation they prove that the complex Hecke algebra of permutation representation is isomorphic to the center of the complex group algebra of \(Sz(s)\). They present a construction of a semi-biplane from any pair ofovoids of \(W(s)\) where in other words a semi-biplane is a Buekenhout diagram geometry of type \(\circ\overset{{}^\subset} {\mathrel{\mkern-8mu}\relbar\joinrel\relbar\mathrel{\mkern-8mu}} \circ\overset{{}^\supset} {\mathrel{\mkern-8mu}\relbar\joinrel\relbar\mathrel{\mkern-8mu}} \circ\). So they get the construction of several new series of that diagram geometries which are embedded as subgeometries of miquelian and Suzuki- Tits inversive planes.
Mathematics Subject Classification ID: 51E25
Mathematics Subject Classification ID: 51E30
zbMATH DE Number: 4122727
zbMATH Keywords: ovoids in symplectic 3-space
zbMATH Keywords: diagram geometry
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90324-4
OpenAlex ID: W1989087044
cites work: Even order inversive planes, generalized quadrangles and codes
cites work: One-step completely orthogonalizable codes from generalized quadrangles
cites work: Two characterizations of even order Miquelian inversive planes
cites work: On the structure of generalized quadrangles
cites work: Simple Groups and Simple Lie Algebras
cites work: The characters of the finite symplectic group Sp(4,q), q=2\(^f\)
cites work: Two multiplicity-free permutation representations of the general linear group \(GL(n,q^ 2)\)
cites work: Q3208669
cites work: Endliche Gruppen I
cites work: Q3659962
cites work: On Möbius-planes of even order
cites work: Q3891315
cites work: Q3344217
cites work: On a class of doubly transitive groups
cites work: Q4739925
Recommended article: On \(m\)-ovoids of symplectic polar spaces
Recommended article: Partial ovoids and partial spreads in symplectic and orthogonal polar spaces
Recommended article: Lagrange intersections in a symplectic space
Recommended article: Q4549280
Recommended article: Q3159718
Recommended article: Odd sphere bundles, symplectic manifolds, and their intersection theory
Recommended article: The Symplectic Geometry of Polygons in the 3-Sphere
Recommended article: Symplectic intersections and invariant measures
Recommended article: Symplectic translation planes and line ovals
Recommended article: ON OVALS OF NON-CONJUGATE SYMMETRIES OF RIEMANN SURFACES
description: scientific article; zbMATH DE number 4122727