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arXiv:2304.13993 [math.RT]AbstractReferencesReviewsResources

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

Nadya Gurevich, David Kazhdan

Published 2023-04-27Version 1

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.

Comments: 25 pages. To appear in Israel Journal of Mathematics
Categories: math.RT
Subjects: 22E50
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