Order and Domains of Attraction of Control Sets in Flag Manifolds
نویسندگان
چکیده
Let G be a real semi-simple noncompact Lie group and S ⊂ G a subsemigroup with intS 6= Ø . This article relates the Bruhat-Chevalley order in the Weyl group W of G to the ordering of the control sets for S in the flag manifolds of G by showing that the one-to-one correspondence between the control sets and the elements of a double coset W (S) \W/WΘ of W reverses the orders. This fact is used to show that the domain of attraction of a control set is a union of Schubert cells.
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