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May 18, 2020 at 12:38 vote accept Mikhail Borovoi
May 18, 2020 at 7:46 answer added Derek Holt timeline score: 6
May 17, 2020 at 22:06 comment added Derek Holt I imagine that the involutive automorphism is the outer automorphism induced within the conformal group ${\rm CSp}(4,3)$, which contains ${\rm Sp}(4,3)$ as a subgroup of index $2$ (some people denote that by ${\rm GSp}(4,3)$ ). I am not really sure what you are asking in Question 1 - there are two 4-dimensional complex representations, which are interchanged by complex conjugation, and also by the outer automorphism. (So the representations are not fixed by complex conjugation, but their images can be chosen so that they are fixed.)
May 17, 2020 at 14:51 history edited Mikhail Borovoi
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May 17, 2020 at 14:38 history edited Mikhail Borovoi CC BY-SA 4.0
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May 17, 2020 at 14:20 history asked Mikhail Borovoi CC BY-SA 4.0