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<p>We prove the uniqueness of the Ginzburg–Rallis models over <i>p</i>-adic local fields of characteristic zero, which completes the local uniqueness problem for the Ginzburg–Rallis models starting from the work of Nien (Models of representations of general linear groups over p-adic fields, ProQuest LLC, Ann Arbor, MI, Thesis (Ph.D.)-University of Minnesota, 2006) that proves the non-split case, and the work of Jiang et al. (Trans Am Math Soc 363(5):2763–2802, 2011) that proves the general case over Archimedean local fields. Our proof extends the strategy of [<CitationRef CitationID="CR16">16</CitationRef>] to the <i>p</i>-adic case with the help of the refined structure of the wavefront sets of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40993_2025_616_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="8" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\mathfrak {z}}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="fraktur">z</mi> </math></EquationSource> </InlineEquation>-finite distributions as developed by Aizenbud et al. (Adv Math 285:1376–1414, 2015).</p>

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Uniqueness of the Ginzburg–Rallis model: the p-adic case

  • 期刊论文

  • 发表日期：

    2025年1月27日

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  • Dihua Jiang,
  • Zhaolin Li,
  • Guodong Xi

摘要

We prove the uniqueness of the Ginzburg–Rallis models over p-adic local fields of characteristic zero, which completes the local uniqueness problem for the Ginzburg–Rallis models starting from the work of Nien (Models of representations of general linear groups over p-adic fields, ProQuest LLC, Ann Arbor, MI, Thesis (Ph.D.)-University of Minnesota, 2006) that proves the non-split case, and the work of Jiang et al. (Trans Am Math Soc 363(5):2763–2802, 2011) that proves the general case over Archimedean local fields. Our proof extends the strategy of [16] to the p-adic case with the help of the refined structure of the wavefront sets of \({{\mathfrak {z}}}\) z -finite distributions as developed by Aizenbud et al. (Adv Math 285:1376–1414, 2015).