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

Ogul Arslan; Peter Sin

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

Representation Theory 2023-05-09 v4 Combinatorics

Authors: Ogul Arslan , Peter Sin

Abstract

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.

Keywords

classical groups weyl modules simple modules p-ranks orthogonal geometry hermitian geometry incidence systems

Cite

@article{arxiv.0908.3035,
  title  = {Some simple modules for classical groups and $p$-ranks of orthogonal and Hermitian geometries},
  author = {Ogul Arslan and Peter Sin},
  journal= {arXiv preprint arXiv:0908.3035},
  year   = {2023}
}

Comments

33 pages, corrected inequality in statement of Thm 1.8 from $n-2\le up\le p+n-3$ to $n-2\le up\le p+n-4$

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

Abstract

Keywords

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