Embeddings of small generalized polygons

Authors:
J. A. Thas;H. Van Maldeghem
Affiliations:
Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000 Ghent, Belgium;Department of Pure Mathematics and Computer Algebra, Ghent University, Galglaan 2, B-9000 Ghent, Belgium
Venue:
Finite Fields and Their Applications
Year:
2006

Citing 3
Cited 2

Embeddings and hyperplanes of discrete geometries

European Journal of Combinatorics
Flat lax and weak lax embeddings of finite generalized hexagons

European Journal of Combinatorics
Full Embeddings Of The Finite Dual Split Cayley Hexagons

Combinatorica

Highest weight modules and polarized embeddings of shadow spaces

Journal of Algebraic Combinatorics: An International Journal
The smallest split Cayley hexagon has two symplectic embeddings

Finite Fields and Their Applications

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Abstract

In this paper we consider some finite generalized polygons, defined over a field with characteristic 2, which admit an embedding in a projective or affine space over a field with characteristic unequal to 2. In particular, we classify the (lax) embeddings of the unique generalized quadrangle H(3,4) of order (4,2). We also classify all (lax) embeddings of both the split Cayley hexagon H(2) and its dual H(2)^d^u^a^l in 13-dimensional projective space PG(13,K), for any skew field K. We apply our results to classify the homogeneous embeddings of these small generalized hexagons, and to classify all homogeneous lax embeddings in real spaces of them. Also, we classify all homogeneous embeddings of generalized quadrangles of order (2,2), (4,2) and (2,4).