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

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

2011-01-05

arxiv.org/abs/1101.1113v1

Mathematics

Group Theory

12 pages

Scientific paper

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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