Representation type of finite quiver Hecke algebras of type $D^{(2)}_{\ell+1}$

TL;DR

This paper classifies the representation types of finite quiver Hecke algebras of affine type D^{(2)}_{ell+1} and computes their stable Auslander-Reiten quivers when not wild.

Contribution

It provides an Erdmann-Nakano type theorem for these algebras, detailing their representation types and methods to analyze their stable Auslander-Reiten quivers.

Findings

Classification of representation types for these algebras.

Identification of conditions for non-wild representation type.

Method to compute stable Auslander-Reiten quivers.

Abstract

We give Erdmann-Nakano type theorem for the finite quiver Hecke algebras $R^{\Lambda_0}(\beta)$ of affine type $D^{(2)}_{\ell+1}$, which tells their representation type. If $R^{\Lambda_0}(\beta)$ is not of wild representation type, we may compute its stable Auslander-Reiten quiver.