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.

arXiv comment23 pages; version that appeared in Representation Theory and erratum added

References in corpus (12)

• Quantum Affine Algebras and their Representations
• Kirillov--Reshetikhin crystals for nonexceptional types
• Minimal Affinizations of Representations of Quantum Groups: the simply--laced case
• Virtual crystals and Kleber's algorithm
• The canonical solutions of the Q-systems and the Kirillov-Reshetikhin conjecture
• Level 1 Perfect Crystals and Path Realizations of Basic Representations at q=0
• Construction of perfect crystals conjecturally corresponding to Kirillov-Reshetikhin modules over twisted quantum affine algebras
• 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
• Bethe Equation at q=0, Moebius Inversion Formula, and Weight Multiplicities: II. X_n case
• Extremal weight modules of quantum affine algebras
• Applications of Crystal Bases to Current Problems in Representation Theory

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• Stable Rigged Configurations for Quantum Affine Algebras of Nonexceptional Types
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• Fusion products of Kirillov-Reshetikhin modules and the X = M conjecture
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• Kirillov-Reshetikhin modules of generalized quantum group of type $A$
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• Similarity and Kirillov-Schilling-Shimozono bijection
• Virtual Crystals and Nakajima Monomials
• Demazure crystals, Kirillov-Reshetikhin crystals, and the energy function
• Perfectness of Kirillov-Reshetikhin Crystals $B^{r,s}$ for types $E_6^{(1)}$ and $E_7^{(1)}$ with a minuscule node $r$
• Ultra-Discretization of $D_6^{(1)}$- Geometric Crystal at the spin node
• Tensor products of Kirillov-Reshetikhin modules and fusion products