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

Marie Dostálová and Petr Somberg

Address: Mathematical Institute of Charles University, Sokolovská 83, Praha 8 - Karlín, Czech Republic


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 ${\mathbb{R}}^2$.

AMSclassification: primary 53C27; secondary 53D05, 81R25.

Keywords: symplectic spin geometry, metaplectic Howe duality, symplectic twistor operator, symplectic Dirac operator.

DOI: 10.5817/AM2013-3-161