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arXiv · 0810.2725

Non-discrete Euclidean Buildings for the Ree and Suzuki groups

Petra Schwer·Linus Kramer·Richard Weiss
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Abstract

We call a non-discrete Euclidean building a Bruhat-Tits space if its automorphism group contains a subgroup that induces the subgroup generated by all the root groups of a root datum of the building at infinity. This is the class of non-discrete Euclidean buildings introduced and studied by Bruhat and Tits. We give the complete classification of Bruhat-Tits spaces whose building at infinity is the fixed point set of a polarity of an ambient building of type B_2, F_4 or G_2 associated with a Ree or Suzuki group endowed with the usual root datum. (In the B_2 and G_2 cases, this fixed point set is a building of rank one; in the F_4 case, it is a generalized octagon whose Weyl group is not crystallographic.) We also show that each of these Bruhat-Tits spaces has a natural embedding in the unique Bruhat-Tits space whose building at infinity is the corresponding ambient building.

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Petra Schwer, Linus Kramer, Richard Weiss. 2009-03-18. Non-discrete Euclidean Buildings for the Ree and Suzuki groups. https://arxiv.org/abs/0810.2725

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