The Auslander-Reiten quivers of string algebras of affine type $\tilde{C}$ and a conjecture by Geiss-Leclerc-Schröer

Abstract

In this paper, we study representations of certain string algebras, which are referred to as of affine type $\tilde{C}$. We introduce minimal string modules and apply them to explicitly describe components of the Auslander-Reiten quivers of the string algebras and $\tau$-locally free modules defined by Geiss-Lerclerc-Schröer. As an application, we prove Geiss-Leclerc-Schröer's conjecture on the correspondence between positive roots of type $\tilde{C}$ and $\tau$-locally free modules of the corresponding string algebras.

21 pages. Any comments are welcome

References in corpus (2)

• Rigid modules and Schur roots
• Quivers with relations for symmetrizable Cartan matrices IV: Crystal graphs and semicanonical functions