AI 中文总结
该论文研究将特定Coxeter群表示为Kac-Moody代数Weyl群的Cartan表示，证明了相关同构条件、有限特征域上的部分结果，明确了晶体学Coxeter群的含义并给出对应Weyl群的条件，还提供了示例。
AI 中文摘要
本论文研究Cartan表示：将特定Coxeter群表示为Kac-Moody代数的Weyl群的表示。文中阐述并证明了这些表示彼此同构、与Coxeter群的反射表示及其对偶表示同构的条件，给出了有限特征域上的部分结果，明确了Coxeter群为晶体学的含义，给出了Kac-Moody代数的Weyl群是晶体学的条件，还提供了若干说明性示例。
英文摘要
This dissertation studies Cartan representations: representations of certain Coxeter groups as the Weyl groups of Kac-Moody algebras. It sets out and proves conditions for these representations to be isomorphic to each other, the reflection representation of the Coxeter group, and their dual representations, and gives partial results for the same over fields of finite characteristic, as well as clarifying what it means for a Coxeter group to be crystallographic and giving conditions for the Weyl group of a Kac-Moody algebra to be such. Some illustrative examples are also provided.
CommentsMSc dissertation, supervised by Dmitriy Rumynin. 46 pages
