Construction of Coassociative submanifolds in $\mathbb{R}^{7}$ and $\Lambda^{2}_{-} S^{4}$ with symmetries

We construct explicit examples of coassociative submanifolds in $\mathbb{R}^{7}$ and $\Lambda^{2}_{-} S^{4}$ invariant under the action of ${\rm SU}(2)$ and $T^{2} \times \mathbb{R}_{>0}$ by the symmetries method.