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

Nadya Gurevich; David Kazhdan

doi:10.1007/s11856-025-2753-y

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

Nadya Gurevich, David Kazhdan

Ben-Gurion University of the Negev, The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	Israel Journal of Mathematics
DOIs	https://doi.org/10.1007/s11856-025-2753-y
State	Accepted/In press - 1 Jan 2025

All Science Journal Classification (ASJC) codes

General Mathematics

Access to Document

10.1007/s11856-025-2753-y

Cite this

@article{e4be9305b18547209f0d61df4fefe5b6,

title = "Fourier transform on a cone and the minimal representation of even orthogonal group",

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.",

author = "Nadya Gurevich and David Kazhdan",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",

year = "2025",

month = jan,

day = "1",

doi = "10.1007/s11856-025-2753-y",

language = "American English",

journal = "Israel Journal of Mathematics",

issn = "0021-2172",

publisher = "Springer New York",

}

TY - JOUR

T1 - Fourier transform on a cone and the minimal representation of even orthogonal group

AU - Gurevich, Nadya

AU - Kazhdan, David

PY - 2025/1/1

Y1 - 2025/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=105002063809&partnerID=8YFLogxK

U2 - 10.1007/s11856-025-2753-y

DO - 10.1007/s11856-025-2753-y

M3 - Article

SN - 0021-2172

JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this