Abstract: In a series of papers with Euiyong Park (and partly with Iijima), we study representation type of the finite quiver Hecke algebra $R^{\Lambda_0}(\beta)$ in various affine Lie types.
In types $ A^{(1)}_\ell$, $A^{(2)}_{2\ell}$ and $D^{(2)}_{\ell+1}$, we have a natural generalization of "$e$-core" and "$e$-weight" for the classical Hecke algebras associated with the symmetric group, and we may give Erdmann-Nakano type theorems. In type $C^{(1)}_\ell$, we do not have such analogues of the $e$-core and the $e$-weight any more. But we may still apply our method developed in our series of papers and I give the result which tells how representation type behaves in type $ C^{(1)}_\ell$.