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arXiv · 2511.19224

Maass-Selberg relations for Whittaker functions on a real reductive group

Erik P. van den Ban
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Abstract

We give a complete proof of the Maass-Selberg relations for Whittaker integrals on a real reductive group. These relations were asserted In unpublished work of Harish-Chandra, and proven in the basic setting of maximal parabolic parabolic subgroups. Our proof is a reduction to the mentioned basic setting. It makes use of the action of standard intertwining operators on Whittaker distribution vectors in the generalized principal series of representations. The Maass-Selberg relations imply regularity of normalized Whittaker integrals. This is crucial for decent behavior of Fourier and wave packet transforms on the level of spherical Schwartz spaces.

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BibTeXRIS

Erik P. van den Ban. 2025-11-24. Maass-Selberg relations for Whittaker functions on a real reductive group. https://arxiv.org/abs/2511.19224

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