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<p>We prove old and new convergence statements for fixed-points statistics and characters of symmetric groups using tensor envelope categories, such as the Deligne–Knop category of representations of the “symmetric group” <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(S_t\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>t</mi> </msub> </math></EquationSource> </InlineEquation> for an indeterminate&#xa0;<i>t</i>. We also speculate on a generalization of Chebotarev’s density theorem to pseudopolynomials.</p>

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Fixed-point statistics from spectral measures on tensor envelope categories

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年10月24日

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  • Arthur Forey,
  • Javier Fresán,
  • Emmanuel Kowalski

摘要

We prove old and new convergence statements for fixed-points statistics and characters of symmetric groups using tensor envelope categories, such as the Deligne–Knop category of representations of the “symmetric group” \(S_t\) S t for an indeterminate t. We also speculate on a generalization of Chebotarev’s density theorem to pseudopolynomials.