PreprintCC BY 4.0arXiv
Standard Representations of Crystallographic Coxeter Groups
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.
Related
- On algebraic dynamics of birational automorphisms of Calabi-Yau manifolds and the universal Coxeter groups
- Cofinite integral braces and crystallographic groups
- Property R∞ for Artin and Coxeter groups whose outer automorphisms are length-preserving
- Bounded Bruhat intervals and affine Coxeter groups
- Quasiparabolic Gelfand models for finite irreducible Coxeter groups and their canonical Hecke structures
BibTeX
@misc{booth2026standard,
title = {{Standard Representations of Crystallographic Coxeter Groups}},
author = {Emma Booth},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04179},
eprint = {2609.04179},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04179},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Standard Representations of Crystallographic Coxeter Groups
AU - Emma Booth
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.04179
UR - https://arxiv.org/abs/2609.04179
AB - 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.
ER -