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

Abstract

We establish a bijection between the set of rigged configurations and the set of tensor products of Kirillov--Reshetikhin crystals of type $D_n^{(1)}$ 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.

54 pages

References in corpus (4)

• Existence of Kirillov-Reshetikhin crystals for nonexceptional types
• Crystal interpretation of Kerov-Kirillov-Reshetikhin bijection
• X=M for symmetric powers
• Combinatorial structure of Kirillov-Reshetikhin crystals of type D_n(1), B_n(1), A_{2n-1}(2)

Cited by in corpus (5)

• Randomized box-ball systems, limit shape of rigged configurations and Thermodynamic Bethe ansatz
• Rigged configuration bijection and proof of the $X=M$ conjecture for nonexceptional affine types
• Rigged configurations and the $\ast$-involution
• A uniform approach to soliton cellular automata using rigged configurations
• Uniform description of the rigged configuration bijection