Quivers for 𝑆𝐿₂ tilting modules

Abstract

Using diagrammatic methods, we define a quiver with relations depending on a prime p \mathsf {p} and show that the associated path algebra describes the category of tilting modules for S L 2 \mathrm {SL}_{2} in characteristic p \mathsf {p} . Along the way we obtain a presentation for morphisms between p \mathsf {p} -Jones–Wenzl projectors.