Degenerate Whittaker functions for $\Sp_n(\R)$

Abstract

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 |$\mathrm{SL}_2(\mathbb{R})$|⁠.

Locations

• International Mathematics Research Notices - View
• Durham Research Online (Durham University) - View - PDF