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In this paper, we construct Whittaker functions with exponential growth for the degenerate principal series of the symplectic group of genus   $n$   induced from the Siegel parabolic subgroup. This is achieved by explicitly constructing a certain Goodman–Wallach operator which yields an intertwining map from the degenerate principal series to the space of Whittaker functions, and by evaluating it on weight-  $\ell$   standard sections. We define a differential operator on such Whittaker functions which can be viewed as generalization of the   $\xi$  -operator on harmonic Maass forms for   $\mathrm{SL}_2(\mathbb{R})$  .

Degenerate Whittaker functions for $\mathrm{Sp}_n(\mathbb{R})$