Type $${{\varvec{D}}}_{{\varvec{n}}}^\mathbf{(1)}$$ rigged configuration bijection

Abstract

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 (1) n . In addition, we establish that the bijection is a classical crystal isomorphism.