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For groups represented as permutations. Group transitivity, rank 3 groups, orbits and suborbits, stablizers, permutation characters, primitivity are all on-topic.

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Does Schur's Lemma hold in this case? Regular representations of $S_n$ over $\mathbb R$

Irreducible representations of $S_n$ are absolutely irreducible, meaning that they remain irreducible after extension of scalars. Therefore, if $V$ is irreducible as an $\mathbb{R} S_n$-module and $\p …
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