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<p>Let <i>G</i> be an even orthogonal quasi-split group defined over a local non-archimedean field <i>F</i>. We describe the subspace of smooth vectors of the minimal representation of <i>G</i>(<i>F</i>), 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年4月3日

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  • Nadya Gurevich,
  • David Kazhdan

摘要

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.