Existence of Kirillov-Reshetikhin crystals for nonexceptional types

TL;DR

This paper proves the existence of Kirillov-Reshetikhin crystals for all nonexceptional affine types using advanced algebraic methods and recent character results, confirming their combinatorial models for certain types.

Contribution

It establishes the existence of Kirillov-Reshetikhin crystals for all nonexceptional affine types and links them to known combinatorial crystals for specific cases.

Findings

Existence of crystals B^{r,s} for all nonexceptional affine types.

Crystals B^{r,s} of types B_n^{(1)}, D_n^{(1)}, and A_{2n-1}^{(2)} are isomorphic to known combinatorial crystals.

Confirmation of the combinatorial models for these crystals.

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.