A bijection between type Dn(1) crystals and rigged configurations
A bijection between type Dn(1) crystals and rigged configurations
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Dn(1) 型晶体和装配结构之间的双射
DOI：
10.1016/j.jalgebra.2004.12.010
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发表时间：
2004
影响因子：
0.9
通讯作者：
A. Schilling
中科院分区：
文献类型：
--
作者：
A. Schilling
Hatayama等人。猜想了与Uq‘(G)-晶体BR，S的张量积有关的费米子公式。晶体BR，S对应于Kirillov-Reshetikhin模，它们是某些有限维Uq’(G)-模。本文给出了Dn(1)型仿射晶体BR，1的组合描述。给出了这些晶体与受操纵组态的晶体路径之间的统计保持双射，从而证明了这种情况下的费米子公式。这个双射反映了统计力学中求解晶格模型的两种不同方法：角点转移矩阵法和Bethe Ansat z法。
Hatayama et al. conjectured fermionic formulas associated with tensor products of Uq′(g)-crystals Br,s. The crystals Br,scorrespond to the Kirillov–Reshetikhin modules which are certain finite-dimensional Uq′(g)-modules. In this paper we present a combinatorial description of the affine crystals Br,1of type Dn(1). A statistic preserving bijection between crystal paths for these crystals and rigged configurations is given, thereby proving the fermionic formula in this case. This bijection reflects two different methods to solve lattice models in statistical mechanics: the corner-transfer-matrix method and the Bethe Ansatz.