Some reductive anisotropic groups that admit no non-trivial split spherical BN-pairs
Group Theory
2011-08-25 v1
Abstract
We prove, for any infinite field k, that any virtually trivial split spherical BN-pair in the group G(k) of k-rational points of a reductive k-group G is already trivial. We then inspect the case when G is k-anisotropic and show that in many situations G(k) admits no non-trivial split spherical BN-pairs. This improves results and contributes to a conjecture of Caprace and Marquis, which can be viewed as a converse to a well-known result of Borel and Tits.
Cite
@article{arxiv.1108.4913,
title = {Some reductive anisotropic groups that admit no non-trivial split spherical BN-pairs},
author = {Peter Abramenko and Matthew C. B. Zaremsky},
journal= {arXiv preprint arXiv:1108.4913},
year = {2011}
}
Comments
11 pages, 1 figure