Path model for representations of generalized Kac-Moody algebras
Path model for representations of generalized Kac-Moody algebras
复制标题
广义 Kac-Moody 代数表示的路径模型
DOI：
10.1016/j.jalgebra.2012.12.028
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发表时间：
2013
影响因子：
0.9
通讯作者：
Motohiro Ishii
中科院分区：
文献类型：
--
作者：
Sano;H.;Kojima;S.;Sato. H.,Martini;R.;Motohiro Ishii
在 [JL] 中，Joseph 和 Lamprou (2009) 将 Littelmann 的 Kac-Moody 代数路径模型推广到广义 Kac-Moody 代数的情况。我们证明，对于由给定广义 Kac-Moody 代数的 Borcherds-Cartan 基准构造的特定 Kac-Moody 代数，Joseph-Lamprou 路径模型可以嵌入到 Littelmann 路径模型中；请注意，这不是晶体的嵌入。使用这种嵌入，我们给出了路径晶体同构定理的新证明，该定理在 Joseph 和 Lamprou (2009) [JL, §7.4] 中获得。此外，对于 Joseph-Lamprou 路径晶体，我们给出了张量积的分解规则和限制 Levi 子代数的分支规则。此外，我们还根据某个幺半群获得了标准路径的表征，可以将其视为 Weyl 群的推广。
In [JL], Joseph and Lamprou (2009) generalized Littelmannʼs path model for Kac–Moody algebras to the case of generalized Kac–Moody algebras. We show that Joseph–Lamprouʼs path model can be embedded into Littelmannʼs path model for a certain Kac–Moody algebra constructed from the Borcherds–Cartan datum of a given generalized Kac–Moody algebra; note that this is not an embedding of crystals. Using this embedding, we give a new proof of the isomorphism theorem for path crystals, obtained in Joseph and Lamprou (2009) [JL, §7.4]. Moreover, for Joseph–Lamprouʼs path crystals, we give a decomposition rule for tensor product and a branching rule for restriction to Levi subalgebras. Also, we obtain a characterization of standard paths in terms of a certain monoid which can be thought of as a generalization of a Weyl group.