Strongly and Weyl transitive group actions on buildings arising from Chevalley groups

Matthew C. B. Zaremsky; Peter Abramenko

arxiv: 1101.1113 · v1 · pith:XLGIOBI2new · submitted 2011-01-05 · 🧮 math.GR

Strongly and Weyl transitive group actions on buildings arising from Chevalley groups

Peter Abramenko , Matthew C. B. Zaremsky This is my paper

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keywords groupweylchevalleydeltaexamplesstronglytransitivelyactions

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Let K be a field and g(K) a Chevalley group (scheme) over K. Let (B,N) be the standard spherical BN-pair in g(K), with T=B\cap N and Weyl group W=N/T. We prove that there exist non-trivial elements w\in W such that all representatives of w in N have finite order. This allows us to exhibit examples of subgroups of g(Q_p) that act Weyl transitively but not strongly transitively on the affine building Delta associated with g(Q_p). Such examples were previously known only in the case when g(Q_p)=SL_2(Q_p) and Delta is a tree.

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