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The strong Centre Conjecture: an invariant theory approach
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Publication details
| Journal | Journal of Algebra |
|---|---|
| Date | E-pub ahead of print - 22 Oct 2012 |
| Date | Published (current) - 15 Dec 2012 |
| Volume | 372 |
| Number of pages | 26 |
| Pages (from-to) | 505-530 |
| Early online date | 22/10/12 |
| Original language | English |
Abstract
The aim of this paper is to describe an approach to a strong 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 by 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 power of this approach by proving the strong form of the Centre Conjecture in some special cases.
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