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On Tensor Products of Simple Modules for Simple Groups, Errata
David A. Craven, University of Birmingham
I distinguish four types of corrections, in order of increasing seriousness:
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(Extra) Additional information that was not available at the time of writing, or that I did not know about.
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(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.
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(Typo) Typographical errors, where I have spelled a word wrongly, used the wrong symbol, and so on.
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(Error) Errors in proofs or statements.
When I give each correction, I will label it with one of these monikers.
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(i) (Error) p.388, just after Proposition 4.7. We do not, in fact, see that all simple modules are algebraic for \(p=2\) for \(\mathfrak {S}_6\) in Theorem 7.3. It is true though, as an easy computer check proves.
Thanks to Daniel Tubbenhauer for pointing this out.
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(ii) (Error) p.388, last paragraph of the section. \(\mathrm {SU}_4(2)\) does not embed in \(\mathrm {SU}_4(2^a)\) for \(a\) even, so this does not prove the result for \(q\) even. While I’m absolutely sure that the statement is true for \(q\) a
power of \(4\), I have no proof at the moment.