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(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.

Keywords
symplectic groups, symplectic grasmmannians, Weyl modules
Mathematical Subject Classification 2010
Primary: 20E42, 20F40, 20G05, 51A45, 51A50
Milestones
Received: 14 June 2010
Accepted: 9 November 2010
Authors
Ilaria Cardinali
Department of Information Engineering and Mathematics
University of Siena
Via Roma 56
53100 Siena
Italy
Antonio Pasini
Department of Information Engineering and Mathematics
University of Siena
Via Roma 56
53100 Siena
Italy