Standard representation of the symmetric group
= Standard representation of the symmetric group
This representation is a distinguished example in the <representation theory of the symmetric group>.
The permutation representation of $S_n$ on $\mathbb C^n$ decomposes as
$$
\mathbb C(1,\ldots,1)
\oplus
\{(x_1,\ldots,x_n):x_1+\cdots+x_n=0\}.
$$
The first summand is the trivial representation and the second is the $(n-1)$-dimensional standard representation.