Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Booth, Emma
Institution: University of Warwick
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7208765099
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