Title: The Permutation Representation of $\Symp(2m,{\Bbb F}_p)$ 
Acting on the Vectors of its Standard Module.

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



Abstract.  This paper studies the permutation representation of a
finite symplectic group over a prime field of odd characteristic on
the vectors of its standard module.  The submodule lattice of this
permutation module is determined. The results yield additive formulae for the $p$-ranks of various incidence matrices arising from the
finite symplectic spaces.

Appeared in J. Algebra  241  (2001),  no. 2, 578--591.