P.S.: I should say am actually interested in involutions of PSU and SO,
but I also need the action on the natural module, so it seems more
convenient to look for involutions of SU and SO. Also, I just discovered
the following papers, which cover the case for PSU(4,q) and PSU(5,q), it
seems -- however I have only access to the second article, thus so far I
only know the solution for PSU(5,q) (funnily, we have the journal in our
library starting with volume 24 -- of course the volume I need is 23 ;-).

http://www.mathnet.or.kr/mathnet/kms_content.php?no=311410
http://www.mathnet.or.kr/mathnet/kms_content.php?no=311495

Also, I was pointed at the paper "Involutions in Chevalley groups over
fields of even order." by Aschbacher and Seitz, which sounds very helpful,
too (assuming I can get hold of it).

Thanks again for your help,
Max

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