Infiniteness of double coset collections in algebraic groups
Let G be a linear algebraic group defined over an algebraically closed field. The double coset question addressed in this paper is the following: Given closed subgroups X and P, is the double coset collection X⧹ G/ P finite or infinite? We limit ourselves to the case where X is maximal rank and redu... Full description
Journal Title:  Journal of Algebra 2004, Vol.273(2), pp.718733 
Main Author:  Duckworth, W.Ethan 
Format:  Electronic Article 
Language: 
English 
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Quelle:  ScienceDirect Journals (Elsevier) 
ID:  ISSN: 00218693 ; EISSN: 1090266X ; DOI: 10.1016/j.jalgebra.2003.08.011 
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title:  Infiniteness of double coset collections in algebraic groups 
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ispartof:  Journal of Algebra, 2004, Vol.273(2), pp.718733 
description:  Let G be a linear algebraic group defined over an algebraically closed field. The double coset question addressed in this paper is the following: Given closed subgroups X and P, is the double coset collection X⧹ G/ P finite or infinite? We limit ourselves to the case where X is maximal rank and reductive and P parabolic. This paper presents a criterion for infiniteness which involves only dimensions of centralizers of semisimple elements. This result is then applied to finish the classification of those X which are spherical subgroups. Finally, excluding a case in F 4, we show that if X⧹ G/ P is finite then X is spherical or the Levi factor of P is spherical. This places great restrictions on X and P for X⧹ G/ P to be finite. The primary method is to descend to calculations at the finite group level and then to use elementary character theory. 
language:  eng 
source:  ScienceDirect Journals (Elsevier) 
identifier:  ISSN: 00218693 ; EISSN: 1090266X ; DOI: 10.1016/j.jalgebra.2003.08.011 
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