A CRYSTAL TO RIGGED CONFIGURATION BIJECTION FOR NONEXCEPTIONAL AFFINE ALGEBRAS
A CRYSTAL TO RIGGED CONFIGURATION BIJECTION FOR NONEXCEPTIONAL AFFINE ALGEBRAS
复制标题
非异常仿射代数的晶体到操纵配置双射
DOI：
10.1142/9789812775405_0005
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发表时间：
2002
影响因子：
0.8
通讯作者：
M. Shimozono
中科院分区：
文献类型：
--
作者：
M. Okado;A. Schilling;M. Shimozono
作者：Okado， Masato；先令,安妮;摘要：对于类型$ a ^{(1)}_n$, Kerov, Kirillov， and Reshetikhin定义了向量表示的张量幂的晶体图中最高权向量与被称为组合构型的组合对象之间的双射。我们为所有非例外仿射类型定义了一个类似的双射，从而证明了（在这种特殊情况下）由Hatayama， Kuniba, Takagi, Tsuboi， Yamada和第一作者推测的费米子公式。
Author(s): Okado, Masato; Schilling, Anne; Shimozono, Mark | Abstract: Kerov, Kirillov, and Reshetikhin defined a bijection between highest weight vectors in the crystal graph of a tensor power of the vector representation, and combinatorial objects called rigged configurations, for type $A^{(1)}_n$. We define an analogous bijection for all nonexceptional affine types, thereby proving (in this special case) the fermionic formulas conjectured by Hatayama, Kuniba, Takagi, Tsuboi, Yamada, and the first author.