Representation type of level 1 KLR algebras \(R^{\Lambda_k}(\beta)\) in type \(C\) (Q6621553)

The paper under review determines the representation type for block algebras \(R^{\Lambda_k}(\beta)\) of the cyclotomic quiver Hecke algebras of type \(C^{(1)}_\ell\), where \(\Lambda_k\) is an arbitrary fundamental weight. It turns out that the representation type is governed by the defect of \(\beta\). This generalises the results of [\textit{S. Ariki} and \textit{E. Park}, Osaka J. Math. 53, No. 2, 463--488 (2016; Zbl 1381.16011)] for finite quiver Hecke algebras of type \(C^{(1)}_\ell\), i.e., for the case \(k=0\).