Type D_n^(1) rigged configuration bijection

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.