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Math Jaxed + further tagged
Daniele Tampieri
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How to find all linear transformations commuting with all elements of the image of an isotypic representation of a compact Lie group

Let a linear finite-dimensional isotypic (i.e., decomposable into a direct sum of isomorphic irreducible subrepresentations) representation of a compact Lie group $G$ in a finite-dimensional space $V$ is given. How to describe all linear transformations of the space $V$, that commute with all elements of the image of this representation? This is probably known. I have my own assumption about this, but I want to know a specific link to the formulation and proof of a way to describe all such transformations

Vladimir47
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