Rigged configurations of type $D_4^{(3)}$ and the filling map

Abstract

We give a statistic preserving bijection from rigged configurations to a tensor product of Kirillov–Reshetikhin crystals $\otimes_{i=1}^{N}B^{1,s_i}$ in type $D_4^{(3)}$ by using virtualization into type $D_4^{(1)}$. We consider a special case of this bijection with $B=B^{1,s}$, and we obtain the so-called Kirillov–Reshetikhin tableaux model for the Kirillov–Reshetikhin crystal.

Keywords

• rigged configuration
• kirillov–reshetikhin crystal
• bijection
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]