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Oct 22, 2014 at 21:29 comment added Derek Holt @MarianoSuárez-Alvarez I think the answer to your question is no, but that is because there is a very nice way of describing the irreducible complex reptns of $S_n$ in terms of Young diagrams, and it is a by-product of this theory that yields the result that they can all be written over the integers.
Oct 22, 2014 at 17:19 comment added Mariano Suárez-Álvarez Is there a way to prove absolute irreducibility without having to find all irreps?
Oct 22, 2014 at 12:29 vote accept vishmay
Oct 22, 2014 at 11:33 history answered David Hill CC BY-SA 3.0