Innovations in Incidence Geometry

On Weyl modules for the symplectic group

Ilaria Cardinali and Antonio Pasini

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Abstract

A rich information can be found in the literature on Weyl modules for Sp ( 2 n , 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 ( 2 n , F ) is uniserial.

Article information

Source
Innov. Incidence Geom., Volume 12, Number 1 (2011), 85-110.

Dates
Received: 14 June 2010
Accepted: 9 November 2010
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323070

Digital Object Identifier
doi:10.2140/iig.2011.12.85

Mathematical Reviews number (MathSciNet)
MR2942719

Zentralblatt MATH identifier
1284.20049

Subjects
Primary: 20E42: Groups with a $BN$-pair; buildings [See also 51E24] 20F40: Associated Lie structures 20G05: Representation theory 51A45: Incidence structures imbeddable into projective geometries 51A50: Polar geometry, symplectic spaces, orthogonal spaces

Keywords
symplectic groups symplectic grasmmannians Weyl modules

Citation

Cardinali, Ilaria; Pasini, Antonio. On Weyl modules for the symplectic group. Innov. Incidence Geom. 12 (2011), no. 1, 85--110. doi:10.2140/iig.2011.12.85. https://projecteuclid.org/euclid.iig/1551323070


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