3rd November, 2020
I distinguish four types of corrections, in order of increasing seriousness:
(Extra) Additional information that was not available at the time of writing, or that I did not know about.
(Improve) Typographical issues, where what is written is still correct, but there is a nicer way of phrasing it, or I could choose a better symbol.
(Typo) Typographical errors, where I have spelled a word wrongly, used the wrong symbol, and so on.
(Error) Errors in proofs or statements.
When I give each correction, I will label it with one of these monikers.
(i) (Improve) The whole paper deals with finite groups. It’s far from clear what happens for arbitrary infinite groups, although some of our analysis will still follow through. For algebraic groups, one can use Steinberg’s restriction theorem to note that a simple highest-weight module for a simple algebraic group is minimally active if and only if the same holds for the fixed points under a suitable Frobenius endomorphism. One may then apply Theorem 2.
(ii) (Error) p.749 In Proposition 20(i), the case \(n\) even cannot occur. Even for \(\mathrm {SL}_4(2).2=\mathrm {Sym}(8)\), the element acts with type \((6,2)\). This is mentioned in a 2014 paper of Lawther–Liebeck–Seitz. While technically I did not state that all cases occur, that is the implication, and indeed the intent.
Thanks to Gunter Malle for noticing this.