Radical layers of representable functors, revisited

The radical layers Theorem was given in a series of two papers of Igusa and Todorov in 1984. This is a very important result which enables us to retrieve various information of the module category from its Auslander-Reiten quiver. It was applied by the authors to give a combinatorial characterization of finite translation quivers which can be realized as Auslander-Reiten quivers. This is a far reaching generalization of Riedtmann’s work for selfinjective algebras using Hom-configurations. In this talk, I will revisit the radical layers Theorem, and explain its applications and also a simple proof which works in a more general setting including triangulated categories.