Siegel $\Phi$ operator (awaiting review)

The Siegel $\Phi$ operator is a linear map that sends degree $g$ Siegel modular forms to degree $g-1$ ones; it is defined by \[ \Phi(f)(\tau) = \lim_{t\to +\infty} f\begin{pmatrix}\tau&0\\0&it\end{pmatrix} \quad \text{for any } \tau \in \mathfrak{H}_{g-1}. \]