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## Combinatorial structure of Kirillov-Reshetikhin crystals of type D_n(1), B_n(1),
A_{2n-1}(2)

- Author(s): Schilling, Anne
- et al.

## Published Web Location

https://arxiv.org/pdf/0704.2046.pdfNo data is associated with this publication.

## Abstract

We provide the explicit combinatorial structure of the Kirillov-Reshetikhin crystals B^{r,s} of type D_n(1), B_n(1), and A_{2n-1}(2). This is achieved by constructing the crystal analogue sigma of the automorphism of the D_n(1) (resp. B_n(1) or A_{2n-1}(2)) Dynkin diagram that interchanges the 0 and 1 node. The involution sigma is defined in terms of new plus-minus diagrams that govern the D_n to D_{n-1} (resp. B_n to B_{n-1}, or C_n to C_{n-1}) branching. It is also shown that the crystal B^{r,s} is perfect. These crystals have been implemented in MuPAD-Combinat; the implementation is discussed in terms of many examples.