# Torsion pairs for quivers and the Weyl groups

Authors
• 1 Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka, 599-8531, Japan , Sakai (Japan)
• 2 Université du Québec à Montréal, Montréal, QC, H3C 3P8, Canada , Montréal (Canada)
Type
Published Article
Journal
Selecta Mathematica
Publisher
Springer International Publishing
Publication Date
Jun 29, 2020
Volume
26
Issue
3
Identifiers
DOI: 10.1007/s00029-020-00563-9
Source
Springer Nature
Keywords
We give an interpretation of the map πc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pi ^c$$\end{document} defined by Reading, which is a map from the elements of a Coxeter group to the c-sortable elements, in terms of the representation theory of preprojective algebras. Moreover, we study a close relationship between c-sortable elements and torsion pairs, and give an explicit description of the cofinite torsion classes in the context of the Coxeter group. As a consequence, we give a proof of some conjectures proposed by Oppermann, Reiten, and the second author.