On Weyl modules for the symplectic group

Abstract

A rich information can be found in the literature on Weyl modules for $Sp\left(2n,\mathbb{F}\right)$, but the most important contributions to this topic mainly enlighten the algebraic side of the matter. In this paper we try a more geometric approach. In particular, our approach enables us to obtain a sufficient condition for a module as above to be uniserial and a geometric description of its composition series when our condition is satisfied. Our result can be applied to a number of cases. For instance, it implies that the module hosting the Grassmann embedding of the dual polar space associated to $Sp\left(2n,\mathbb{F}\right)$ is uniserial.