On the universal embedding of the near hexagon related to the extended ternary Golay code

Yoshiara [Embeddings of flag-transitive classical locally polar geometries of rank 3, Geom. Dedicata 43 (1992) 121-165] and Bardoe [On the universal embedding of the near-hexagon for U"4(3), Geom. Dedicata 56 (1995) 7-17] showed that the embedding rank ...

The generating rank is determined for several GF(2)-embeddable geometries and it is demonstrated that their generating and embedding ranks are equal. Specifically, we prove that each of the two generalized hexagons of order (2, 2) has generating rank 14,...

Given a (thick) irreducible spherical building $\mathrm{\Omega }$, we establish a bound on the difference between the generating rank and the embedding rank of its long root geometry and the dimension of the corresponding Weyl module, by showing that this ...$\mathrm{}$${\mathsf{}}_{}$${\mathsf{}}_{\mathsf{}\mathsf{}}$