Work

Coxeter embeddings are injective

Year: 2024

Type: preprint

Abstract: We show that certain embeddings of Coxeter groups within other Coxeter groups are injective using the notion of Coxeter partitions. Moreover, we study Lusztig's partitions, which are generalizations of Lusztig's admissible maps and Crisp's foldings. We show that they classify the simplest type of Coxeter partitions, whose embeddings of Coxeter groups send each generator to a product of commuting generators. Consequently, these embeddings are also injective, and we prove that they preserve Coxeter numbers. These results were previously known, due to work of Mühlherr and Dyer.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2402.00974

Authors: Elias, Ben, Heng, Edmund

Institutions: University of Oregon, Institut des Hautes Études Scientifiques

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Awards: Categorical and Diagrammatic Representation Theory, RTG: Combinatorics, Geometry, Representation Theory, and Topology at University of Oregon

OpenAlex ID: W4391555554

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