Infiniteness of double coset collections in algebraic groups

  title={Infiniteness of double coset collections in algebraic groups},
  author={William Duckworth},
  journal={Journal of Algebra},
  • W. Duckworth
  • Published 18 May 2003
  • Mathematics
  • Journal of Algebra
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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