Geometriae Dedicata

, Volume 35, Issue 1, pp 389–436

The Bruhat order on symmetric varieties

  • R. W. Richardson
  • T. A. Springer

DOI: 10.1007/BF00147354

Cite this article as:
Richardson, R.W. & Springer, T.A. Geom Dedicata (1990) 35: 389. doi:10.1007/BF00147354


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.

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • R. W. Richardson
    • 1
  • T. A. Springer
    • 2
  1. 1.School of Mathematical SciencesAustralian National UniversityCanberraAustralia
  2. 2.Mathematisch Instituut, Rijksuniversiteit UtrechtUtrechtThe Netherlands

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