English

On Reflection Representations of Coxeter Groups over Non-Commutative Rings

Representation Theory 2021-07-06 v1

Abstract

In this paper, we consider representations of Coxeter groups over a path algebra, R, defined by Dyer. We answer a question posed by Dyer about the multiplicative properties of R, showing that it is "almost a domain". We also show that R cam be embedded in a matrix ring over a free product of extension fields of the rational numbers and rings of Laurent polynomials.

Keywords

Cite

@article{arxiv.2107.01530,
  title  = {On Reflection Representations of Coxeter Groups over Non-Commutative Rings},
  author = {Annette Pilkingtonn},
  journal= {arXiv preprint arXiv:2107.01530},
  year   = {2021}
}

Comments

28 pages

R2 v1 2026-06-24T03:52:17.926Z