Affine crystal structure on rigged configurations of type D_n^(1)

Extending the work in Schilling (Int. Math. Res. Not. 2006:97376, 2006 ), we introduce the affine crystal action on rigged configurations which is isomorphic to the Kirillov–Reshetikhin crystal B r , s of type D_n^(1) for any r , s . We also introduce a representation of B r , s ( r ≠ n −1, n ) in terms of tableaux of rectangular shape r × s , which we coin Kirillov–Reshetikhin tableaux (using a nontrivial analogue of the type A column splitting procedure) to construct a bijection between elements of a tensor product of Kirillov–Reshetikhin crystals and rigged configurations.