no. 3
Quiver presentations and Schur–Weyl duality for Khovanov arc algebras
Bowman, Christopher David1 orcid ; De Visscher, Maud2; Dell’Arciprete, Alice3; Hazi, Amit4 orcid; Muth, Robert W.5 orcid; Stroppel, Catharina Helene6
1Department of Mathematics, University of York, Heslington, York, UK
2Department of Mathematics, City St George’s, University of London, London, UK
3Ruhr-Universität Bochum, Fakultät für Mathematik, Universitätstraße 150, 44780 Bochum, Germany
4School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK
5Department of Mathematics and Computer Science, Duquesne University, Pittsburgh, PA 15282, USA
6Mathematical Institute, Endenicher Allee 60, 53115 Bonn, Germany
Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 509-563

We provide an $\operatorname{Ext}$-quiver and relations presentation of the Khovanov arc algebras and as an application we prove a precise analogue of the Kleshchev–Martin conjecture in this setting.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/art.49
Classification: 05E10, 16G20, 17B10, 18N25, 20C08
Keywords: Khovanov arc algebras, quiver and relations

Bowman, Christopher David  1 ; De Visscher, Maud  2 ; Dell’Arciprete, Alice  3 ; Hazi, Amit  4 ; Muth, Robert W.  5 ; Stroppel, Catharina Helene  6

1 Department of Mathematics, University of York, Heslington, York, UK
2 Department of Mathematics, City St George’s, University of London, London, UK
3 Ruhr-Universität Bochum, Fakultät für Mathematik, Universitätstraße 150, 44780 Bochum, Germany
4 School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK
5 Department of Mathematics and Computer Science, Duquesne University, Pittsburgh, PA 15282, USA
6 Mathematical Institute, Endenicher Allee 60, 53115 Bonn, Germany
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
Bowman, Christopher David; De Visscher, Maud; Dell’Arciprete, Alice; Hazi, Amit; Muth, Robert W.; Stroppel, Catharina Helene. Quiver presentations and Schur–Weyl duality for Khovanov arc algebras. Annals of Representation Theory, Volume 3 (2026) no. 3, pp. 509-563. doi: 10.5802/art.49
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