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

TL;DR

This paper provides a combinatorial formula for the graded dimension of finite quiver Hecke algebras of type C^{(1)}_ell and establishes a criterion to determine their representation type.

Contribution

It introduces a new combinatorial dimension formula and a simple criterion for classifying the representation type of these algebras.

Findings

Graded dimension formula expressed via Young diagrams

Simple criterion for representation type classification

Enhanced understanding of algebraic structure in type C^{(1)}_ell

Abstract

We give a graded dimension formula described in terms of combinatorics of Young diagrams and a simple criterion to determine the representation type for the finite quiver Hecke algebras of type $C_{\ell}^{(1)}$.