If you consider the permutation representation of Sn in ℂ^n, i.e the transformation which takes a permutation into the operator which uses it to permute the coordinates of a vector, then of course the subspace such that every coordinate of the vector is the same is invariant under the representation. Also, the subspace in which all coordinates sum to zero is invariant. But are there any others that are independent of these ones?(adsbygoogle = window.adsbygoogle || []).push({});

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# Basic Symmetric Group Representation Question

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