The Symplectic Fueter-Sce Theorem

Abstract

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.

"Sce" added in the title; moreover, we added more motivation and intuition and rewrote some proofs in more detail; 19 pages, 1 figure