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The Bruhat order on symmetric varieties

Identifieur interne : 002222 ( Main/Merge ); précédent : 002221; suivant : 002223

The Bruhat order on symmetric varieties

Auteurs : R. W. Richardson [Australie] ; T. A. Springer [Pays-Bas]

Source :

RBID : ISTEX:0E28236CE2C89F7545A918E6555828113D4BFC59

English descriptors

Abstract

Abstract: Let G be a connected reductive linear algebraic group over an algebraically closed field of characteristic not 2. Let θ be an automorphism of order 2 of the algebraic group G. Denote by K the fixed point group of θ and by B a Borel group of G. It is known that the number of double cosets BgK is finite. This paper gives a combinatorial description of the inclusion relations between the Zariski-closures of such double cosets. The description can be viewed as a generalization of Chevalley's description of the inclusion relations between the closures of double cosets BgB, which uses the Bruhat order of the corresponding Weyl group.

Url:
DOI: 10.1007/BF00147354

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ISTEX:0E28236CE2C89F7545A918E6555828113D4BFC59

Le document en format XML

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<div type="abstract" xml:lang="en">Abstract: Let G be a connected reductive linear algebraic group over an algebraically closed field of characteristic not 2. Let θ be an automorphism of order 2 of the algebraic group G. Denote by K the fixed point group of θ and by B a Borel group of G. It is known that the number of double cosets BgK is finite. This paper gives a combinatorial description of the inclusion relations between the Zariski-closures of such double cosets. The description can be viewed as a generalization of Chevalley's description of the inclusion relations between the closures of double cosets BgB, which uses the Bruhat order of the corresponding Weyl group.</div>
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