Representation type of cyclotomic quiver Hecke algebras of type $C_{\ell }^{(1)}$

Abstract

We first investigate a connected quiver consisting of all dominant maximal weights for an integrable highest weight module in affine type C. This quiver provides an efficient method to obtain all dominant maximal weights. Then, we completely determine the representation type of cyclotomic Khovanov-Lauda-Rouquier algebras of arbitrary level in affine type C, by using the quiver we construct. We also determine the Morita equivalence classes and graded decomposition matrices of certain representation-finite and tame cyclotomic KLR algebras.

This article has been withdrawn and no more revised version will be updated. There are two reason for this: 1. Section 1-4 are parallel to the well-known facts in affine type A with slight modifications, 2. a gap on decomposition matrices appear in the last section