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 Sp2n(K) to the naturally embedded subgroup Sp2n−2(K) is determined. As a corollary, inductive systems of fundamental representations for Sp∞(K) are classified. The submodule structure of the fundamental Weyl modules is refined. 2000 Mathematics Subject Classification 20G05. [ABSTRACT FROM AUTHOR]