A crystal to rigged configuration bijection and the filling map for type

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• 作者：Travis Scrimshaw¹ ; ^{tscrimsh@umn.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：05E10 ; 17B37
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 February 2016
• 年：2016
• 卷：448
• 期：Complete
• 页码：294-349
• 全文大小：832 K

文摘

We give a bijection Φ from rigged configurations to a tensor product of Kirillov–Reshetikhin crystals of the form B^r,1$B^{r,1}$ and B^1,s$B^{1,s}$ in type $D_4^{(3)}$. We show that the cocharge statistic is sent to the energy statistic for tensor products ${⨂}_{i=1}^N{B}^{r_i,1}$ and 233cd619416256bd5">${⨂}_{i=1}^N{B}^{1,s_i}$. We extend this bijection to a single B^r,s$B^{r,s}$, show that it preserves statistics, and obtain the so-called Kirillov–Reshetikhin tableaux model for B^r,s$B^{r,s}$. Additionally, we show that Φ commutes with the virtualization map and that B^1,s$B^{1,s}$ is naturally a virtual crystal in type $D_4^{(1)}$, thus defining an affine crystal structure on rigged configurations corresponding to B^1,s$B^{1,s}$.