A Classification of Certain Finite Double Coset Collections in the Classical Groups

W. Ethan Duckworth

A Classification of Certain Finite Double Coset Collections in the Classical Groups

Group Theory 2007-05-23 v1

Authors: W. Ethan Duckworth

Abstract

Let $G$ be a classical algebraic group, $X$ a maximal rank reductive subgroup and $P$ a parabolic subgroup. This paper classifies when $X\G/P$ is finite. Finiteness is proven using geometric arguments about the action of $X$ on subspaces of the natural module for $G$ . Infiniteness is proven using a dimension criterion which involves root systems.

Keywords

classical algebraic groups reductive subgroups parabolic subgroups double cosets finiteness root systems natural module

Cite

@article{arxiv.math/0309446,
  title  = {A Classification of Certain Finite Double Coset Collections in the Classical Groups},
  author = {W. Ethan Duckworth},
  journal= {arXiv preprint arXiv:math/0309446},
  year   = {2007}
}

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14 pages

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