Representation type of higher level cyclotomic quiver Hecke algebras in affine type C

Ariki, Susumu; Hudak, Berta; Song, Linliang; Wang, Qi

doi:10.5802/art.34

Ariki, Susumu ¹ ; Hudak, Berta ²; Song, Linliang ³; Wang, Qi ⁴

¹Osaka University (retired)
²Okinawa Institute of Science and Technology, Okinawa, 904-0495, Japan
³School of Mathematical Science & Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University, Shanghai, 200092, China
⁴School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

Annals of Representation Theory, Volume 3 (2026) no. 1, pp. 27-97

Abstract

We determine the representation type of cyclotomic quiver Hecke algebras of affine type C. In the tame cases, we explicitly describe their basic algebras under the assumption $\operatorname{char}\mathbb{k}\ne 2$, relying on the Morita invariance of cellularity.

Received: 2024-07-14
Revised: 2025-11-10
Accepted: 2025-12-15
Published online: 2026-02-05

DOI: 10.5802/art.34

Classification: 20C08, 16G60, 17B65, 16G20
Keywords: Cyclotomic KLR algebras, cyclotomic quiver Hecke algebras, representation type, Brauer graph algebras, silting theory, derived equivalence

Author's affiliations:

Ariki, Susumu ¹ ; Hudak, Berta ² ; Song, Linliang ³ ; Wang, Qi ⁴

¹ Osaka University (retired)
² Okinawa Institute of Science and Technology, Okinawa, 904-0495, Japan
³ School of Mathematical Science & Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University, Shanghai, 200092, China
⁴ School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     title = {Representation type of higher level cyclotomic quiver {Hecke} algebras in affine type {C}},
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Ariki, Susumu; Hudak, Berta; Song, Linliang; Wang, Qi. Representation type of higher level cyclotomic quiver Hecke algebras in affine type C. Annals of Representation Theory, Volume 3 (2026) no. 1, pp. 27-97. doi: 10.5802/art.34

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