Symplectic twistor operator and its solution space on ${\mathbb{R}}^2$

Abstract

We introduce the symplectic twistor operator $T_s$ in symplectic spin geometry, as a symplectic analogue of the twistor operator in Riemannian spin geometry. We focus on the real dimension 2 and compute the space of its solutions on ${\mathbb{R}}^2$. Our analysis is based on the techniques of metaplectic Howe duality.