Symplectic twistor operator and its solution space on $\mR^2$

Abstract

We introduce the symplectic twistor operator $T_s$ in symplectic spin geometry of real dimension two, as a symplectic analogue of the Dolbeault operator in complex spin geometry of complex dimension $1$. Based on the techniques of the metaplectic Howe duality and algebraic Weyl algebra, we compute the space of its solutions on $\mR^2$.

Keywords

• Symplectic spin geometry
• Metaplectic Howe duality
• Symplectic twistor operator
• Symplectic Dirac operator.