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<p>A <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="209_2025_3720_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textbf{GL}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="bold">GL</mi> </math></EquationSource> </InlineEquation><i>-variety</i> is a (typically infinite dimensional) variety modeled on the polynomial representation theory of the general linear group. In previous work, we studied these varieties in characteristic&#xa0;0. In this paper, we obtain results in positive characteristic: for example, we prove a version of Chevalley’s theorem on constructible sets. We give an application of our theory to strength of polynomials.</p>

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The geometry of polynomial representations in positive characteristic

  • 期刊论文

  • 发表日期：

    2025年3月22日

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  • Arthur Bik,
  • Jan Draisma,
  • Andrew Snowden

摘要

A \(\textbf{GL}\) GL -variety is a (typically infinite dimensional) variety modeled on the polynomial representation theory of the general linear group. In previous work, we studied these varieties in characteristic 0. In this paper, we obtain results in positive characteristic: for example, we prove a version of Chevalley’s theorem on constructible sets. We give an application of our theory to strength of polynomials.