Existence of Kirillov-Reshetikhin crystals for nonexceptional types

Abstract

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} is established for all nonexceptional affine types. We also prove that the crystals B^{r,s} of type B_n^{(1)}, D_n^{(1)}, and A_{2n-1}^{(2)} are isomorphic to recently constructed combinatorial crystals for r not a spin node.

23 pages; version that appeared in Representation Theory and erratum added

References in corpus (3)

• Combinatorial structure of Kirillov-Reshetikhin crystals of type D_n(1), B_n(1), A_{2n-1}(2)
• Proof of the combinatorial Kirillov-Reshetikhin conjecture
• Applications of Crystal Bases to Current Problems in Representation Theory

Cited by in corpus (4)

• Combinatorial structure of Kirillov-Reshetikhin crystals of type D_n(1), B_n(1), A_{2n-1}(2)
• Hecke group algebras as quotients of affine Hecke algebras at level 0
• A generalization of adjoint crystals for the quantized affine algebras of type $A\sb{n}\sp{(1)}$, $C\sb{n}\sp{(1)}$ and $D\sb{n+1}\sp{(2)}$
• A crystal theoretic method for finding rigged configurations from paths