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A Quasi Curtis-Tits-Phan theorem for the symplectic group

Rieuwert J. Blok·Corneliu Hoffman
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Abstract

We obtain the symplectic group as an amalgam of low rank subgroups akin to Levi components. We do this by having the group act flag-transitively on a new type of geometry and applying Tits' lemma. This provides a new way of recognizing the symplectic groups from a small collection of small subgroups. The geometry consists of all subspaces of maximal rank in a vector space of maximal rank with respect to a symplectic form. The main result holds for fields of size at least 3. We analyze the geometry over the field of size 2 and describe its simply connected cover if different from the geometry.

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Rieuwert J. Blok, Corneliu Hoffman. 2006-04-12. A Quasi Curtis-Tits-Phan theorem for the symplectic group. https://arxiv.org/abs/math/0604300

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