English

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.

Keywords

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

R2 v1 2026-06-21T12:57:17.979Z