I'm reading the paper 'Bruinier, Jan Hendrik; Funke, Jens, On two geometric theta lifts. Duke Math. J. 125 (2004), no. 1, 45–90.' In p.52, they say that
We denote by $\omega=\omega_V$ the Schrödinger model of the (restriction of the) Weil representation of $G' \times O(V(\mathbb R))$ acting on $S(V(\mathbb R))$, the space of Schwartz functions on $V(\mathbb R)$.
Here I don't have the knowledge about 'Schroedinger model', 'Weil representation', and 'Schwartz function'. Could you give me a proper reference?