Determinant representation
= Determinant representation
{title2=$\det V=\Lambda^{\dim V}V$}
The top <exterior power> of an $n$-dimensional <group representation> is one-dimensional, and $g$ acts on it by $\det R(g)$. It is trivial for the defining <representation> of $SU(n)$. This is why a full $n$-box column in an $SU(n)$ <Young diagram> can be removed without changing the <representation>.