Irreducible Representations of SO(3) and the Laplacian

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IntroductionIn our previous post on theirreducible representations of \(SU(2)\) and \(SO(3)\), the irreducible representations of\(SU(2)\) has been determinedexplicitly: \(V_n=\operatorname{Sym}^n\mathbb{C}^2\), andirreducible representations \(W_n\) of\(SO(3)\) correspond to \(V_{2n}\).The result i……