Branching rules for modular fundamental representations of symplectic groups

In this paper, branching rules for the fundamental representations of the symplectic groups in positive characteristic are found. The submodule structure of the restrictions of the fundamental modules for the group Sp(2n)(K) to the naturally embedded subgroup Sp(2n-2)(K) is determined. As a corollary, inductive systems of fundamental representations for Sp(infinity)(K) are classified. The submodule structure of the fundamental Weyl modules is refined.