The Symplectic Fueter–Sce Theorem

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.