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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{}}$

Let E"1 be the near hexagon on 729 points related to the extended ternary Golay code. We prove in an entirely geometric way that the generating and embedding ranks of E"1 are equal to 24. We also study the structure of the universal embedding e@? of E"...

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 ...