Existence of Kirillov–Reshetikhin crystals for nonexceptional types

Using the methods of Kang et al. and recent results on the characters of Kirillov–Reshetikhin modules by Nakajima and Hernandez, the existence of Kirillov–Reshetikhin crystals B r , s B^{r,s} is established for all nonexceptional affine types. We also prove that the crystals B r , s B^{r,s} of type B n ( 1 ) B_n^{(1)} , D n ( 1 ) D_n^{(1)} , and A 2 n − 1 ( 2 ) A_{2n-1}^{(2)} are isomorphic to recently constructed combinatorial crystals for r r not a spin node.