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Invariant theory deals with an algebraic, geometric or analytic structure $X$, submitted to the action of an (algebraic) group $G$. It studies $G$-invariant elements of $X$ as well as the set of $G$-orbits.

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The Casimir invariant of an irreducible representation of a compact Lie group

[I started to type this as a comment but it took like ten comments to fit, so I paste it into an answer. It is an answer as it explains how you can use the references you already have to answer your q …
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