Title: On the Doubly Transitive Permutation Representations of 
$\Sp(2n,\mathbb F_2$)

Authors: N.S. Narasimha Sastry
                       Math.-Stat. Division, 
                       Indian Statistical Institute
                       8th Mile, Mysore Road, R.V. College Post 
                       Bangalore - 560 059, India

 Peter Sin
                        Department of Mathematics
                        University of Florida 
                        358 Little Hall
                        PO Box 118105
                        Gainesville, FL 32611-8105 


Abstract. Each symplectic group over the field of two elements has two
exceptional doubly transitive actions on 
sets of quadratic forms on the defining symplectic
vector space. This paper studies the associated $2$-modular permutation modules.
Filtrations of these modules are constructed which have subquotients
which are modules for the symplectic group over an algebraically closed field
of characteristic $2$ and which, as such, have filtrations by Weyl modules and 
dual Weyl modules having fundamental
highest weights. These Weyl modules have known
submodule structures. It is further shown that the submodule
structures of the Weyl modules are unchanged when restricted to the finite subgroups 
$\Sp(2n,2)$ and $\Orth^\pm(2n,2)$.


Preprint