Restricted limits of minimal affinizations
Restricted limits of minimal affinizations
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DOI：
10.2140/pjm.2010.244.359
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发表时间：
2008-12
影响因子：
0.6
通讯作者：
A. Moura
中科院分区：
文献类型：
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作者：
A. Moura
我们得到了当基础单李代数正交且最大权值的支持包含在Dynkin图的前三个节点时，量子群表示的最小亲和的特征公式。我们还提供了一个框架，将我们的技术扩展到更一般的情况。特别地，对于正交代数和最多支持一个自旋节点的最高权，我们实现了相应的最小亲和的受限经典极限作为由生成器和关系给出的模的商，并进一步证明了它投射到由适当的受限Kirillov-Reshetikhin模的张量积的顶权空间所生成的子模上。我们还证明了Chari和Pressley关于D - 4型中某些最小亲和的等价性的一个猜想。
We obtain character formulas of minimal affinizations of representations of quantum groups when the underlying simple Lie algebra is orthogonal and the support of the highest weight is contained in the first three nodes of the Dynkin diagram. We also give a framework for extending our techniques to a more general situation. In particular, for the orthogonal algebras and a highest weight supported in at most one spin node, we realize the restricted classical limit of the corresponding minimal affinizations as a quotient of a module given by generators and relations and, furthermore, show that it projects onto the submodule generated by the top weight space of the tensor product of appropriate restricted Kirillov-Reshetikhin modules. We also prove a conjecture of Chari and Pressley regarding the equivalence of certain minimal affinizations in type D 4 .