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.

中文翻译：

---

辛Fueter–Sce定理

在本文中，我们提出了Fueter定理的辛类似物。这允许构造辛Dirac算子\（D_s \）的特殊（多项式）解，定义为一阶\（\ mathfrak {sp}（2n）\）-作用于\上函数的不变微分算子（\ mathbb {R} ^ {2n} \）取值在干ple状棘肌表示中。