Subgroup Structure and Representations of Finite and Algebraic Groups

Some remarks on maximal subgroups of finite classical groups

“…In those cases where one can show that e 1 + e 2 2 one can use the results of Magaard, Malle and Tiep [27] to achieve the conclusion of Theorem 2.3. We note that if W is a Weil module for H = Sp 2r (3), then unpublished work of Tiep and Magaard (see also [36]) shows that Λ 3 (W ) and Sym 3 (W ) are irreducible H-modules, indicating that the bound e 1 + e 2 2 can not hold universally.…”

“…The possibilities (G 2 (2 a ), Sp 6 (2 a )) were completely classified by Schaeffer-Fry [32]. Also see Tiep [36] for further discussion of this case.…”

“…The study of the maximal subgroups of finite groups provides a very good illustration of this and the reader is referred to Aschbacher's article in these proceedings [1] for a general overview and context. The survey article by Tiep [36] also provides an excellent introduction to this topic as well as a host of applications. In this note we remark on the current state of affairs of the classification of the maximal subgroups of the finite classical groups and illustrate things with some examples.…”