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On the doubly transitive permutation representations of Sp(2n,F2)

โœ Scribed by N.S.Narasimha Sastry; Peter Sin

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
184 KB
Volume
257
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

Each symplectic group over the field of two elements has two exceptional doubly transitive actions on sets of quadratic forms on the defining symplectic vector space. This paper studies the associated 2-modular permutation modules. Filtrations of these modules are constructed which have subquotients which are modules for the symplectic group over an algebraically closed field of characteristic 2 and which, as such, have filtrations by Weyl modules and dual Weyl modules having fundamental highest weights. These Weyl modules have known submodule structures. It is further shown that the submodule structures of the Weyl modules are unchanged when restricted to the finite subgroups Sp(2n, 2) and O ยฑ (2n, 2).

๐Ÿ“œ SIMILAR VOLUMES

The Permutation Representation of Sp(2m,
The Permutation Representation of Sp(2m, Fp) Acting on the Vectors of Its Standard Module
โœ Peter Sin ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 120 KB

This paper studies the permutation representation of a finite symplectic group over a prime field of odd characteristic on the vectors of its standard module. The submodule lattice of this permutation module is determined. The results yield additive formulae for the p-ranks of various incidence matr