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.

Source : oai:HAL:hal-01337783v1

Volume: DMTCS Proceedings, 27th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2015)

Section: Proceedings

Published on: January 1, 2015

Submitted on: November 21, 2016

Keywords: rigged configuration,Kirillov–Reshetikhin crystal,bijection,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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