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Adhérence de Zariski des groupes de Coxeter

Published online by Cambridge University Press:  04 December 2007

Yves Benoist  and
Pierre de la Harpe
Yves Benoist
Affiliation:
École Normale Supérieure, 45 rue d'Ulm, 75230 Paris, Francebenoist@dma.ens.fr
Pierre de la Harpe
Affiliation:
Section de Mathématiques, Université de Genève, C.P. 240, CH-1211 Genève 24, SwitzerlandPierre.delaHarpe@math.unige.ch
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Abstract

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We describe the Zariski closure of the geometric realization of Coxeter groups. When the Coxeter system is irreducible and the Tits form B non-positive and non-degenerate, this Zariski closure is equal to the orthogonal group of B.

Keywords

Coxeter groupsTits representationZariski closure20F55 (primary)22E40 (secondary)

Information

Type
Research Article
Information
Compositio Mathematica , Volume 140 , Issue 5 , September 2004 , pp. 1357 - 1366
Copyright
Foundation Compositio Mathematica 2004