The permutation action of finite symplectic groups of odd characteristic on their standard modules

Details The permutation action of finite symplectic groups of odd characteristic on their standard modules The permutation action of finite symplectic groups of odd characteristic on their standard modules

2006-03-03

arxiv.org/abs/math/0603100v1

Mathematics

Combinatorics

22 pages

Scientific paper

Motivated by the incidence problems between points and flats of a symplectic polar space, we study a large class of submodules of the space of functions on the standard module of a finite symplectic group of odd characteristic. Our structure results on this class of submodules allow us to determine the $p$-ranks of the incidence matrices between points and flats of the symplectic polar space. In particular, we give an explicit formula for the $p$-rank of the generalized quadrangle ${\rm W}(3,q)$, where $q$ is an odd prime power. Combined with the earlier results of Sastry and Sin on the 2-rank of ${\rm W}(3,2^t)$, it completes the determination of the $p$-ranks of ${\rm W}(3,q)$.

Affiliated with

Also associated with

No associations

Rating

The permutation action of finite symplectic groups of odd characteristic on their standard modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The permutation action of finite symplectic groups of odd characteristic on their standard modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The permutation action of finite symplectic groups of odd characteristic on their standard modules will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-618890