On the monoidal center of Deligne's category Re̲p(St)

Flake, Johannes; Laugwitz, Robert

Abstract

We explicitly compute a monoidal subcategory of the monoidal center of Deligne’s interpolation category Rep(St), for t not necessarily a natural number, and we show that this subcategory is a ribbon category. For t = n, a natural number, there exists a functor onto the braided monoidal category of modules over the Drinfeld double of Sn which is essentially surjective and full. Hence the new ribbon categories interpolate the categories of crossed modules over the symmetric groups. As an application, we obtain invariants of framed ribbon links which are polynomials in the interpolating variable t. These polynomials interpolate untwisted Dijkgraaf–Witten invariants of the symmetric groups.

Citation

Flake, J., & Laugwitz, R. (2021). On the monoidal center of Deligne's category Re̲p(St). Journal of the London Mathematical Society, 103(3), 1153-1185. https://doi.org/10.1112/jlms.12403

• Journal Article Type: Article
• Acceptance Date: Nov 6, 2020
• Online Publication Date: Dec 4, 2020
• Publication Date: 2021-04
• Deposit Date: Nov 9, 2020
• Publicly Available Date: Dec 4, 2020
• Journal: Journal of the London Mathematical Society
• Print ISSN: 0024-6107
• Electronic ISSN: 1469-7750
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 103
• Issue: 3
• Pages: 1153-1185
• DOI: https://doi.org/10.1112/jlms.12403
• Keywords: 18M15 (primary), 05E10 , 57K14 (secondary)
• Public URL: https://nottingham-repository.worktribe.com/output/5030952
• Publisher URL: https://londmathsoc.onlinelibrary.wiley.com/doi/abs/10.1112/jlms.12403
• Additional Information: Received: 2019-11-02; Published: 2020-12-04