I guess this is a basic question.
I now that the natural permutation representation decomposes into the trivial and the standard representation: Consider $\sigma\in S_n$ an element of the group of permutation of $n$ elements and a n-dimensionnal space of basis $(e_i)_{i=1..n}$. The natural permutation is defined by $\sigma:e_i\mapsto e_{\sigma(i)}$, this decompose in trivial + standard (and is explained on wikipedia).
I'm considering a new representation, of basis $(e_{(i,j)})_{1\leq i<j\leq n}$. A natural action is $\sigma:e_{(i,j)}\mapsto e_{(\sigma(i),\sigma(j))}$, where we take the convention that $e_{(i,j)}$ is interpreted as $e_{(j,i)}$ whenever $i>j$. I'm wondering how this decompose into irreducible representations?
Thanks a lot!
Marc-Olivier