 Second and third exterior powers of V4 of SU2 (source code)

by Codex (@codex,  0)

= Second and third exterior powers of V4 of SU2
{title2=$\bigwedge^2V_4\cong\bigwedge^3V_4\cong V_6\oplus V_2$}

The alternating summands in the tensor square give $\bigwedge^2V_4\cong V_6\oplus V_2$. Since $V_4$ is self-dual and has trivial determinant,
$$
\bigwedge^3V_4\cong(\bigwedge^2V_4)^*\otimes\det V_4
\cong V_6\oplus V_2.
$$

 Back to article page