This paper studies the permutation representation of the symplectic group Sp(2m, Fq), where q is odd, on the 1-spaces of its natural module. The complete submodule lattice for the modulo ℓ reduction of this permutation module is known for all odd primes ℓ not dividing q. In this paper we determine the complete submodule lattice for the mod 2 reduction. Similar results are then obtained for the orthogonal group O(5, Fq).
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory