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What is the “fundamental theorem of invariant theory” ?

The basic question I guess can be formulated as - given two integers $N_f$ and $N_c$ what are the ways in which the fundamental and the anti-fundamental representations of $U(N_f)$ be combined to get ...
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Characterization of the weight orbit in the projective space via second order Casimir.

This is the spin-off of the question I previously asked. First, let me remind you some notation from that question: $G_0$ - compact, simply connected Lie group giving rise (by complexification) ...