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The strong Centre Conjecture: an invariant theory approach

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JournalJournal of Algebra
DateE-pub ahead of print - 22 Oct 2012
DatePublished (current) - 15 Dec 2012
Volume372
Number of pages26
Pages (from-to)505-530
Early online date22/10/12
Original languageEnglish

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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