1) I would prefer that you
say yourself that your magic triangle is not the one of M theory but
rather extends the one of Tits, so that people do not get the false
impression that you did it right and first.
You did it right for some
invariant theory problem that is special and connects to other things than
my triangle and you know CJ did not know your preprint E7 came as
70+63=133 for us!

2) I propose that you use the terminology contragredient to not commit
yourself too soon to unitary representations the complex conjugations are
to be avoided for instance avoid conjugate multiplet with your definition
it should come with complex conjugation

p2
p3 dual space should be DEFINED without cc it turns out equal

p4 the Kronecker is always an invariant the quadratic form or hermitian
form is what defines SO or SU or SH=USP groups
IF YOU STICK TO YOUR NOTATION YOU STICK TO SUBGROUPS OF O(N) for no reason

bottom of p6 there are r+1 invariants in your list

also the definition of combination is not clear in def at top of 2.5

More later form an average physicist!


Bernard L. JULIA  ENS-CNRS/LPT
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