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The aim of our article is the study of solution space of the symplectictwistor operator $T_s$ in symplectic spin geometry on standard symplectic space$({\mathbb R}^{2n},\omega)$, which is the symplectic analogue of the twistoroperator in (pseudo)Riemannian spin geometry. In particular, we observe asubstantial difference between the case $n=1$ of real dimension 2 and the caseof ${\mathbb R}^{2n}$, $n>1$. For $n>1$, the solution space of $T_s$ isisomorphic to the Segal-Shale-Weil representation.

Symplectic twistor operator on ${\mathbb R}^{2n}$ and the Segal-Shale-Weil representation