Actually, all of these representations are defined over $\mathbb{Q}$ (i.e., they are absolutely indecomposable).  This is stated in the second sentence of the Encyclopedia of Math article on [Representation of the symmetric groups](https://www.encyclopediaofmath.org/index.php/Representation_of_the_symmetric_groups). This follows immediately from the fact that the Young symmetrizer is defined over $\mathbb{Q}$ (and thus also $\mathbb{R}$).