One of the fundamental orthogonality theorems in the representation theory of finite groups. (Which I studied in the late 1970s with much joy.) #HappyNewYear #algebra #mathpic.twitter.com/HF06RbfBry
I had always seen the definition of irreducible representation as “containing no non-trivial π(G)-invariant subspace”.. while that’s fine, it’s a bit dense.. I had never seen the definition that says its center contains only matrices proportional to identity.. Very cool
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Thanks for your note. The definition I gave follows by Schur's Lemma but it isn't quite equivalent to the definition of irreducible (which you noted). So we should go with the invariant subspace. (I'm use to working with unitary representations where the definition I gave works.)
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Ah, very useful clarification. Thanks!
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