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May 22, 2020 at 10:06 comment added Quarto Bendir I mean the group $\text{O}(V^{\otimes n},g_{\otimes n})$
May 22, 2020 at 9:58 comment added Mikhail Borovoi What do you mean by $g_{\otimes n}$-invariant linear maps? Invariant with respect to what group?
May 22, 2020 at 9:49 comment added Mikhail Borovoi Assertion 1 is about linear maps, so it holds over $\Bbb R$ if and only if it holds over $\Bbb C$, and hence it has nothing to do with positive definiteness of $g$.
May 22, 2020 at 9:39 comment added Ben McKay You might look at Claudio Procesi's book Lie Groups, where a lot of classical invariant theory is explained in a convenient modern language.
May 22, 2020 at 9:11 history asked Quarto Bendir CC BY-SA 4.0