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

Flake, Johannes; Laugwitz, Robert


Johannes Flake


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.


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.

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
Keywords 18M15 (primary), 05E10 , 57K14 (secondary)
Public URL
Publisher URL
Additional Information Received: 2019-11-02; Published: 2020-12-04


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