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

TL;DR

This paper introduces the symplectic twistor operator in symplectic spin geometry, focusing on solutions in two dimensions using metaplectic Howe duality, and explores its properties and solution space.

Contribution

It defines the symplectic twistor operator and computes its solution space on 2, providing new insights into symplectic spin geometry and operator analysis.

Findings

Solution space characterized on 2

Application of metaplectic Howe duality techniques

Establishment of symplectic twistor operator properties

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.