# Infiniteness of double coset collections in algebraic groups

@article{Duckworth2003InfinitenessOD, title={Infiniteness of double coset collections in algebraic groups}, author={William Duckworth}, journal={Journal of Algebra}, year={2003}, volume={273}, pages={718-733} }

Abstract 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…

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