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arXiv · 2304.13993

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

Nadya Gurevich·David Kazhdan
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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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BibTeXRIS

Nadya Gurevich, David Kazhdan. 2023-04-27. Fourier transform on a cone and the minimal representation of even orthogonal group. https://arxiv.org/abs/2304.13993

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