Affine crystal structure on rigged configurations of type \(D_{n}^{(1)}\) (Q1947193)

In this paper the authors introduce an affine crystal action on rigged configurations corresponding to a single Kirillov-Reshetikhin crystal \(B^{r,s}\) of type \(D_n^{(1)}\) for any \(r\) and \(s\). Additionally, the authors show that the associated crystal isomorphism preserves the grading by energy and cocharge. Furthermore, the authors introduce a representation of \(B^{r,s}\) in terms of tableaux of rectangular shape \(r\times s\) and construct a bijection between elements of a tensor product of Kirillov-Reshetikhin crystals and rigged configurations. This is achieved using a new explicit combinatorial algorithm generalizing the type \(A\) column splitting.