For the irreps (Gamma^{(1)}, Gamma^{(2)}), and (Gamma^{(3)}) of the group (mathrm{S}_{3}), determine the irrep content of the

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For the irreps \(\Gamma^{(1)}, \Gamma^{(2)}\), and \(\Gamma^{(3)}\) of the group \(\mathrm{S}_{3}\), determine the irrep content of the nine direct products \(\Gamma^{(n)} \otimes \Gamma^{(m)}\).

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