Torsion pairs for quivers and the Weyl groups

2018/04/06 by Yuya Mizuno, Hugh Thomas, Mizuno, Yuya +1
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1804.02148

openalex publication_date 2018/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an interpretation of the map π^c 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.

Related

• Coxeter groups and quiver representations
• Preprojective roots of Coxeter groups
• Sortable Elements for Quivers with Cycles
• Tilting theory of preprojective algebras and c-sortable elements
• Preprojective representations of valued quivers and reduced words in the Weyl group of a Kac-Moody algebra