Existence of Kirillov-Reshetikhin crystals for near adjoint nodes in exceptional types
Existence of Kirillov-Reshetikhin crystals for near adjoint nodes in exceptional types
复制标题
特殊类型中近伴随节点基里洛夫-列谢蒂欣晶体的存在
DOI：
10.1016/j.jpaa.2020.106593
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发表时间：
2021
影响因子：
0.8
通讯作者：
Travis Scrimshaw
中科院分区：
文献类型：
--
作者：
Katsuyuki Naoi;Travis Scrimshaw
利用Kang等人提出的判别准则，证明了在E6，7，8（1），F4（1）和E6（2）型中，每一个与伴随节点相邻的Kirillov-Reshetikhin模（近伴随节点）都有一个晶体伪基.我们通过使用极值权重模块的全局基来实现这一点。
We prove that, in types E 6, 7, 8 (1), F 4 (1) and E 6 (2), every Kirillov–Reshetikhin module associated with the node adjacent to the adjoint one (near adjoint node) has a crystal pseudobase, by applying the criterion introduced by Kang et al. In order to apply the criterion, we need to prove some statements concerning values of a bilinear form. We achieve this by using the global bases of extremal weight modules.