Preprojective roots and graph monoids of Coxeter groups

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Certain results on representations of quivers have analogs in the structure theory of general Coxeter groups. A fixed Coxeter element turns the Coxeter graph into an acyclic quiver, allowing for the definition of a preprojective root. A positive root is an analog of an indecomposable representation of the quiver. The Coxeter group is finite if and only if every positive root is preprojective, which is analogous to the well-known result that a quiver is of finite representation type if and only if every indecomposable representation is preprojective. Combinatorics of orientation-admissible words in the graph monoid of the Coxeter graph relates strongly to reduced words and the weak order of the group.

Original languageEnglish (US)
Title of host publicationRepresentations of Algebras, Geometry and Physics
EditorsKiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov
PublisherAmerican Mathematical Society
Pages85-110
Number of pages26
ISBN (Print)9781470452308
DOIs
StatePublished - 2021
EventMaurice Auslander Distinguished Lectures and International Conference, 2018 - Falmouth, United States
Duration: Apr 25 2018Apr 30 2018

Publication series

NameContemporary Mathematics
Volume769
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Conference

ConferenceMaurice Auslander Distinguished Lectures and International Conference, 2018
Country/TerritoryUnited States
CityFalmouth
Period4/25/184/30/18

ASJC Scopus subject areas

  • Mathematics(all)

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