Three combinatorial models for affine sl(n) crystals, with applications to cylindric plane partitions
Three combinatorial models for affine sl(n) crystals, with applications to cylindric plane partitions
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仿射 sl(n) 晶体的三种组合模型，及其在圆柱平面分区中的应用
DOI：
10.1093/imrn/rnm143
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
P. Tingley
中科院分区：
文献类型：
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作者：
P. Tingley
我们定义了三个组合模型的\hat{sl（n）}晶体，参数化分区，配置珠上的算盘，圆柱形平面分区，分别。这些都是可约的，但我们可以确定一个不可约的亚晶体对应于任何占主导地位的积分最高的重量。双曲平面划分实际上参数化了不可约表示与所有划分所跨越的空间的张量积的基础。我们用它来计算一个系统的随机圆柱形平面分区的配分函数。我们还观察到一种等级二元性的形式。最后，我们使用一个明确的双射，我们的工作与京都路径模型。
We define three combinatorial models for \hat{sl(n)} crystals, parametrized by partitions, configurations of beads on an `abacus', and cylindric plane partitions, respectively. These are reducible, but we can identify an irreducible subcrystal corresponding to any dominant integral highest weight. Cylindric plane partitions actually parametrize a basis for the tensor product of an irreducible representation with the space spanned by all partitions. We use this to calculate the partition function for a system of random cylindric plane partitions. We also observe a form of rank level duality. Finally, we use an explicit bijection to relate our work to the Kyoto path model.