references for faithful orthogonal (or unitary) representation of symmetric groups

Let $S_n$ be the symmetric group of $n$ points. I want to find references (or proofs) for the following statement (1).

(1). There does not exist any faithful orthogonal representation $$S_n\longrightarrow O(n-2).$$

In order to prove (1), I want to use the result that any unitary representation of $S_n$ is over $\mathbb{Q}$ and find references or proofs for the following statement (2).

(2). There does not exist any faithful unitary representation $$S_n\longrightarrow U(n-2).$$

Where to find references for (1)?

(if cannot, then find references for (2)? )

The smallest degree faithful representation of $S_n$ is $n-1$ in characteristic does not divide $n$. It is Theorem 22 of Chapter 19, Section 8 of Y. G. Berkovich, E. M. Zhmud; Characters of finite groups. Part 2. Translated from the Russian manuscript by P. Shumyatsky, V. Zobina and Berkovich. Translations of Mathematical Monographs, 181. American Mathematical Society, Providence, RI, 1999.
• That is the case in characteristic $0$. It can certainly be found in the book of G.D. James. – Geoff Robinson Oct 9 '15 at 10:26