#### Vol. 12, No. 1, 2011

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On Weyl modules for the symplectic group

### Ilaria Cardinali and Antonio Pasini

Vol. 12 (2011), No. 1, 85–110
##### 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.

##### Keywords
symplectic groups, symplectic grasmmannians, Weyl modules
##### Mathematical Subject Classification 2010
Primary: 20E42, 20F40, 20G05, 51A45, 51A50