The smallest split Cayley hexagon has two symplectic embeddings

  • Authors:

  • K. Coolsaet

  • Affiliations:

  • Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281-S9, B-9000 Gent, Belgium

  • Venue:
  • Finite Fields and Their Applications
  • Year:
  • 2010

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Abstract

It is well known that the smallest split Cayley generalized hexagon H(2) can be embedded into the symplectic space W(5,2), or equivalently, into the parabolic quadric Q(6,2). We establish a second way to embed H(2) into the same space and describe a computer proof of the fact that these are essentially the only two embeddings of this type.