Symplectic contraction of an exterior square
= Symplectic contraction of an exterior square
For a <symplectic vector space> $(V,\omega)$, contraction is the map $c:\Lambda^2V\to\mathbb C$ defined by $c(v\wedge w)=\omega(v,w)$. It is equivariant for the <symplectic Lie algebra>. In dimension four its five-dimensional <kernel> is irreducible of <highest weight> $\omega_2$, while the invariant inverse-form bivector spans a complementary <trivial Lie algebra representation>.