Fourier transform on a cone and the minimal representation of even orthogonal group

2023/04/27 by Nadya Gurevich, David Kazhdan, Gurevich, Nadya +1 · 3 citations
Mathematics · #Mathematical Analysis and Transform Methods #Advanced Algebra and Geometry #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2304.13993

Abstract

Let G be an even orthogonal quasi-split group defined over a local non-archimedean field F. We describe the subspace of smooth vectors of the minimal representation of G(F), realized on the space of square-integrable functions on a cone. Our main tool is the Fourier transform on the cone, for which we give an explicit formula.

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