The strong Centre Conjecture: an invariant theory approach

Details The strong Centre Conjecture: an invariant theory approach The strong Centre Conjecture: an invariant theory approach

2010-05-18

arxiv.org/abs/1005.3212v3

Mathematics

Group Theory

30 pages, minor changes, new subsection on rationality; v3 updated bibliography and affiliation of second author

Scientific paper

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.

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