Fundamental representations of sl3 ($V({\omega }_1)={\mathbb{C}}^3,V({\omega }_2)={\Lambda }^2{\mathbb{C}}^3$)

The two fundamental representations of ${\mathfrak{sl}}_3$ are the defining representation $V({\omega }_1)={\mathbb{C}}^3$ and its dual

For the defining representation $V=V({\omega }_1)$ of ${\mathfrak{sl}}_3$,