  In this paper we present a symplectic analogue of the Fueter theorem. This
allows the construction of special (polynomial) solutions for the symplectic
Dirac operator $D_s$, which is defined as the first-order
$\mathfrak{sp}(2n)$-invariant differential operator acting on functions on
${\mathbb R}^{2n}$ taking values in the metaplectic spinor representation.
