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arXiv · 1603.08121

Type $D_n^{(1)}$ rigged configuration bijection

Masato Okado·Reiho Sakamoto·Anne Schilling·Travis Scrimshaw
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Abstract

We establish a bijection between the set of rigged configurations and the set of tensor products of Kirillov--Reshetikhin crystals of type $D^{(1)}_n$ in full generality. We prove the invariance of rigged configurations under the action of the combinatorial $R$-matrix on tensor products and show that the bijection preserves certain statistics (cocharge and energy). As a result, we establish the fermionic formula for type $D_n^{(1)}$. In addition, we establish that the bijection is a classical crystal isomorphism.

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Masato Okado, Reiho Sakamoto, Anne Schilling, Travis Scrimshaw. 2016-03-26. Type $D_n^{(1)}$ rigged configuration bijection. https://doi.org/10.1007/s10801-017-0756-4

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