Fourier transforms on the basic affine space of a quasi-split group
Representation Theory
2023-04-28 v3
Abstract
We extend the Gelfand and Graev construction of generalized Fourier transforms on basic affine space from split groups to quasi-split groups over a local non-archimedean field .
Cite
@article{arxiv.1912.07071,
title = {Fourier transforms on the basic affine space of a quasi-split group},
author = {Nadya Gurevich and David Kazhdan},
journal= {arXiv preprint arXiv:1912.07071},
year = {2023}
}
Comments
The previous version has been split in two papers. To define the generalized Fourier transform for SU(3) we use the formula for the Fourier transform on a 5-dimensional cone, from our paper "Fourier transform on a cone and the minimal representation of even orthogonal group", where the general cone is treated. Some proofs have been simplified. To appear in Israel Journal of Mathematics