Arboreal tensor categories

• Nate Harman ^[1] ; Ilia Nekrasov ^[2] ; Andrew Snowden ^[3]
  1. [1] University of Georgia

     University of Georgia

     Estados Unidos

     
  2. [2] University of California System

     University of California System

     Estados Unidos

     
  3. [3] University of Michigan–Ann Arbor

     University of Michigan–Ann Arbor

     City of Ann Arbor, Estados Unidos

     

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 3, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01058-1
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• Resumen

  • We introduce some new symmetric tensor categories based on the combinatorics of trees: a discrete family D(n), for n ≥ 3 an integer, and a continuous family C(t), for t = 1 a complex number. The construction is based on the general oligomorphic theory of Harman–Snowden, but relies on two non-trivial results we establish. The first determines the measures for the class of trees, and the second is a semi-simplicity theorem. These categories have some notable properties: for instance, C(t) is the first example of a 1-parameter family of pre-Tannakian categories of superexponential growth that cannot be obtained by interpolating categories of moderate growth.

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