Subdivision of KLRW Algebras in Affine Type A

In this paper, we consider the subdivision map between two KLRW algebras of type A⁽¹⁾ₑ and A⁽¹⁾ₑ₊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.