Existence of Kirillov-Reshetikhin crystals for nonexceptional types

Details Existence of Kirillov-Reshetikhin crystals for nonexceptional types Existence of Kirillov-Reshetikhin crystals for nonexceptional types

2007-06-15

arxiv.org/abs/0706.2224v4

Represent.Theory12:186-207,2008

Mathematics

Quantum Algebra

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

Scientific paper

10.1090/S1088-4165-08-00329-4

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.

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