Maass-Selberg relations for Whittaker functions on a real reductive group
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915635248758784 |
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| author | Ban, Erik P. van den |
| author_facet | Ban, Erik P. van den |
| contents | 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 These relations were asserted In unpublished work of Harish-Chandra, and proven in the basic setting of maximal parabolic parabolic subgroups.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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_19224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maass-Selberg relations for Whittaker functions on a real reductive group Ban, Erik P. van den Representation Theory primary: 22E46, secondary 43A30, 43A85 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 These relations were asserted In unpublished work of Harish-Chandra, and proven in the basic setting of maximal parabolic parabolic subgroups.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. |
| title | Maass-Selberg relations for Whittaker functions on a real reductive group |
| topic | Representation Theory primary: 22E46, secondary 43A30, 43A85 |
| url | https://arxiv.org/abs/2511.19224 |