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The indecomposable objects in the center of Deligne's category Rep St

Flake, Johannes; Harman, Nate; Laugwitz, Robert

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Authors

Johannes Flake

Nate Harman



Abstract

We classify the indecomposable objects in the monoidal center of Deligne's interpolation category Rep St by viewing Rep St as a model‐theoretic limit in rank and characteristic. We further prove that the center of Rep St is semisimple if and only if t is not a non‐negative integer. In addition, we identify the associated graded Grothendieck ring of this monoidal center with that of the graded sum of the centers of representation categories of finite symmetric groups with an induction product. We prove analogous statements for the abelian envelope.

Citation

Flake, J., Harman, N., & Laugwitz, R. (2023). The indecomposable objects in the center of Deligne's category Rep St. Proceedings of the London Mathematical Society, 126(4), 1134-1181. https://doi.org/10.1112/plms.12509

Journal Article Type Article
Acceptance Date Nov 23, 2022
Online Publication Date Jan 11, 2023
Publication Date 2023-04
Deposit Date Apr 5, 2023
Publicly Available Date Apr 5, 2023
Journal Proceedings of the London Mathematical Society
Print ISSN 0024-6115
Electronic ISSN 1460-244X
Publisher London Mathematical Society
Peer Reviewed Peer Reviewed
Volume 126
Issue 4
Pages 1134-1181
DOI https://doi.org/10.1112/plms.12509
Public URL https://nottingham-repository.worktribe.com/output/16216867
Publisher URL https://londmathsoc.onlinelibrary.wiley.com/doi/10.1112/plms.12509
Additional Information Received: 2021-06-10; Accepted: 2022-11-23; Published: 2023-01-11

Files

The indecomposable objects in the center of Deligne's category Re ̲ p S t $\protect\underline{{\rm Re}}\!\operatorname{p}S_t$ (548 Kb)
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Publisher Licence URL
https://creativecommons.org/licenses/by-nc/4.0/

Copyright Statement
This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.





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