A Fueter operator for 3/2-spinors

We show the non-compactness of moduli space of solutions of the monopole equations for $3\mathrm{/}2$-spinors on a closed 3-manifold is equivalent to the existence of `3/2-Fueter sections’ that are solutions of an overdetermined non-linear elliptic differential equation. These are sections of a fiber bundle whose fiber is a special 4-dimensional submanifold of the hyperkähler manifold of center-framed charged one $SU(2)$-instantons on ${\mathbf{R}}^4$. This fiber bundle does not inherit a hyperkähler structure.