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Journal of the London Mathematical Society 1998 58(1):63-83; doi:10.1112/S0024610798006310
© 1998 by London Mathematical Society
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© The London Mathematical Society

Double Coset Density in Exceptional Algebraic Groups

Jonathan Brundan

Department of Mathematics, 1222 University of Oregon Eugene, OR 97403, USA. E-mail: brundan{at}darkwing.uoregon.edu

Received 2 October 1995. Revision received 15 February 1996.

Let G be a simple algebraic group of exceptional type, defined over an algebraically closed field K of characteristic p≥0. In this paper, we classify all pairs (X, Y) of reductive subgroups of G which have a dense (X, Y)-double coset in G. In fact, we show that there is a dense (X, Y)-double coset in G precisely when G=XY is a factorisation. The possible factorisations that can occur have recently been determined in [11, Theorem A].

We now state our main result.


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