Fixed-point statistics from spectral measures on tensor envelope categories
Abstract 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” $$S_t$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mi>t</mml:mi> </mml:msub> </mml:math> for an indeterminate t . We also speculate on a generalization of Chebotarev’s density theorem to pseudopolynomials.
Authors
- Arthur Forey (ORCID: https://orcid.org/0000-0002-5999-3831)
- Emmanuel Kowalski (ORCID: https://orcid.org/0009-0009-8487-8729)
- Javier Fresán (ORCID: https://orcid.org/0000-0002-8550-6646)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université Paris Cité (FR)
- Université de Lille (FR)
- Institut de Mathématiques de Jussieu-Paris Rive Gauche (FR)
- ETH Zurich (CH)
- Sorbonne Université (FR)
- Centre de Mathématiques Laurent Schwartz (FR)
- Laboratoire Paul Painlevé (FR)
- Laboratoire de Physique des Plasmas (FR)
Publication Details
- Journal
- Selecta Mathematica
- Published
- 2025-10-24
- DOI
- https://doi.org/10.1007/s00029-025-01091-0
- Primary Topic
- Tensor decomposition and applications
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Agence Nationale de la Recherche
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- Eidgenössische Technische Hochschule Zürich