The strong Centre Conjecture: an invariant theory approach
Group Theory
2011-12-19 v3 Algebraic Geometry
Metric Geometry
Abstract
The aim of this paper is to describe an approach to a a strengthened form of J. Tits' Centre Conjecture for spherical buildings. This is accomplished by generalizing a fundamental result of G. R. Kempf from Geometric Invariant Theory and interpreting this generalization in the context of spherical buildings. We are able to recapture the conjecture entirely in terms of our generalization of Kempf's notion of a state. We demonstrate the utility of this approach by proving the Centre Conjecture in some special cases.
Keywords
Cite
@article{arxiv.1005.3212,
title = {The strong Centre Conjecture: an invariant theory approach},
author = {Michael Bate and Benjamin Martin and Gerhard Roehrle},
journal= {arXiv preprint arXiv:1005.3212},
year = {2011}
}
Comments
30 pages, minor changes, new subsection on rationality; v3 updated bibliography and affiliation of second author