Weighted Coxeter graphs and generalized geometric representations of Coxeter Groups
Vadim Bugaenko, Yonah Cherniavsky, Tatiana Nagnibeda, Robert Shwartz

TL;DR
This paper introduces weighted Coxeter graphs and a generalized geometric representation of Coxeter groups, providing conditions for faithfulness and exploring connections to the numbers game, advancing understanding of Coxeter group representations.
Contribution
It defines weighted Coxeter graphs and develops a generalized geometric representation, including criteria for faithfulness and links to the numbers game.
Findings
Provided sufficient conditions for faithfulness of the representation
Established the relationship between balanced graphs and the numbers game
Extended the standard geometric representation to weighted graphs
Abstract
We introduce the notion of weighted Coxeter graph and associate to it a certain generalization of the standard geometric representation of a Coxeter group. We prove sufficient conditions for faithfulness and non-faithfulness of such a representation. In the case when the weighted Coxeter graph is balanced we discuss how the generalized geometric representation is related to the numbers game played on the Coxeter graph.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · graph theory and CDMA systems
