Strongly and Weyl transitive group actions on buildings arising from Chevalley groups
Group Theory
2011-01-07 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1101.1113,
title = {Strongly and Weyl transitive group actions on buildings arising from Chevalley groups},
author = {Peter Abramenko and Matthew C. B. Zaremsky},
journal= {arXiv preprint arXiv:1101.1113},
year = {2011}
}
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12 pages