Fourier transforms on the basic affine space of a quasi-split group

TL;DR

This paper extends the construction of generalized Fourier transforms from split to quasi-split groups over local non-archimedean fields, broadening the applicability of harmonic analysis techniques.

Contribution

It introduces a new framework for Fourier transforms on basic affine spaces of quasi-split groups, generalizing previous work on split groups.

Findings

Extended Fourier transform construction to quasi-split groups

Broadened harmonic analysis tools for non-split groups

Provided foundational groundwork for further representation theory studies

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 $F$.