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

  • Author(s): Okado, Masato
  • Sakamoto, Reiho
  • Schilling, Anne
  • Scrimshaw, Travis
  • et al.

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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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