Homological stability for classical groups
K-Theory and Homology
2012-09-05 v5 Group Theory
Abstract
Associated to every group with a weak spherical Tits system of rank n+1 with an appropriate rank n subgroup, we construct a relative spectral sequence involving group homology of Levi subgroups of both groups. Using the fact that such Levi subgroups frequently split as semidirect products of smaller groups, we prove homological stability results for unitary groups over division rings with infinite centre as well as for special linear and special orthogonal groups over infinite fields.
Cite
@article{arxiv.0905.0071,
title = {Homological stability for classical groups},
author = {Jan Essert},
journal= {arXiv preprint arXiv:0905.0071},
year = {2012}
}
Comments
30 pages; shortened homology part, polishing