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.
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To Jacques Tits on the occasion of his sixtieth birthday
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Richardson, R.W., Springer, T.A. The Bruhat order on symmetric varieties. Geom Dedicata 35, 389–436 (1990). https://doi.org/10.1007/BF00147354
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DOI: https://doi.org/10.1007/BF00147354