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arXiv:0908.3035 [math.RT]AbstractReferencesReviewsResources

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

Ogul Arslan, Peter Sin

Published 2009-08-20, updated 2023-05-06Version 4

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.

Comments: 33 pages, corrected inequality in statement of Thm 1.8 from $n-2\le up\le p+n-3$ to $n-2\le up\le p+n-4$
Categories: math.RT, math.CO
Subjects: 20G05, 05E10
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