Generalized Green Functions and Unipotent Classes for Finite Reductive Groups, I
Generalized Green Functions and Unipotent Classes for Finite Reductive Groups, I
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DOI：
10.1017/s0027763000009338
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发表时间：
2005-07
影响因子：
0.8
通讯作者：
David Hernandez;Hiraku Nakajima
中科院分区：
文献类型：
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作者：
David Hernandez;Hiraku Nakajima
我们研究了由第二作者定义的单晶。我们证明了单晶的每个组分都可以嵌入到由柏原引入的极值权模的晶体中。我们确定了所有出现在对应于量子仿射代数的所有0级基本表示的分量中的单项式，除了的一些节点。因此，我们在这些例子中得到了晶体的明确描述。我们也给出了相应的有限维表示。对于经典的类型，我们以场景的形式给它们。对于特殊类型，我们列出所有的单项式。
We study the monomial crystal defined by the second author. We show that each component of the monomial crystal can be embedded into a crystal of an extremal weight module introduced by Kashiwara. And we determine all monomials appearing in the components corresponding to all level 0 fundamental representations of quantum affine algebras except for some nodes of . Thus we obtain explicit descriptions of the crystals in these examples. We also give those for the corresponding finite dimensional representations. For classical types, we give them in terms of tableaux. For exceptional types, we list up all monomials.