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A CLASSIFICATION OF CERTAIN FINITE DOUBLE COSET COLLECTIONS IN THE CLASSICAL GROUPS

Published online by Cambridge University Press:  19 October 2004

W. ETHAN DUCKWORTH
W. ETHAN DUCKWORTH
Affiliation:
Mathematics Department, Rutgers University, Piscataway, NJ 08854, USAduck@math.rutgers.edu
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Abstract

Let $G$ be a classical algebraic group, $X$ a maximal rank reductive subgroup and $P$ a parabolic subgroup. This paper classifies when $X\backslash G/P$ 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 that involves root systems.

Keywords

14L3014L3520G15
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 6 , November 2004 , pp. 758 - 768
Copyright
© The London Mathematical Society 2004

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