I am writing a paper(physics) where I am using the fact that the irreducible's of the regular representations of the permutation group are absolutely irreducible in the following sense.
If $V$ is an irreducible of the regular representation of $S_n$ over $R$ (real numbers) then it remain irreducible under the extension of the field to complex numbers $ C$.
In particular,I only need the fact that they remain irreducible when we go from $R$ to $C$.
Q1) Firstly , is this TRUE?
Q2) Can anyone please provide a reference where this is explicitly mentioned? (if possible also where in the text it appears)