Representation type of finite quiver Hecke algebras of type A2ℓ(2)

We study cyclotomic quiver Hecke algebras RΛ0(β)RΛ0(β) in type A2ℓ(2), where Λ0Λ0 is the fundamental weight. The algebras are natural A2ℓ(2)-type analogue of Iwahori–Hecke algebras associated with the symmetric group, from the viewpoint of the Fock space theory developed by the first author and his collaborators. We give a formula for the dimension of the algebra, and a simple criterion to tell the representation type. The criterion is a natural generalization of Erdmann and Nakanoʼs for the Iwahori–Hecke algebras. Except for the examples coming from cyclotomic Hecke algebras, no results of these kind existed for cyclotomic quiver Hecke algebras, and our results are the first instances beyond the case of cyclotomic Hecke algebras.