Subdivision of KLRW Algebras in Affine Type A

In this paper, we consider the subdivision map between two KLRW algebras of type $A_e^{(1)}$ and $A_{e+1}^{(1)}$. We show that the image of an idempotent indexed by a partition under this map is still an idempotent indexed by a partition, and give the form of this new partition. Moreover, we give an equality of some graded decomposition numbers.