On Weyl modules for the symplectic group

A rich information can be found in the literature on Weyl modules for Sp(2n,F), 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(2n,F) is uniserial. © 2011, Mathematical Sciences Publishers. All rights reserved.