Some simple modules for classical groups and $p$-ranks of orthogonal and Hermitian geometries

Details Some simple modules for classical groups and $p$-ranks of orthogonal and Hermitian geometries Some simple modules for classical groups and $p$-ranks of orthogonal and Hermitian geometries

2009-08-20

arxiv.org/abs/0908.3035v3

Mathematics

Representation Theory

33 pages, corrected parity of u in statement of Theorem 1.6(b)

Scientific paper

We determine the characters of the simple composition factors and the
submodule lattices of certain Weyl modules for classical groups. The results
have several applications. The simple modules arise in the study of incidence
systems in finite geometries and knowledge of their dimensions yields the
$p$-ranks of these incidence systems.

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