Quivers for SL(2) tilting modules

TL;DR

This paper introduces a diagrammatic quiver algebra associated with SL(2) tilting modules in characteristic p, providing a new algebraic framework and explicit morphism presentations.

Contribution

It defines a novel quiver algebra for SL(2) tilting modules in characteristic p using diagrammatic methods, including a presentation for morphisms between p-Jones-Wenzl projectors.

Findings

The quiver algebra models the category of SL(2) tilting modules in characteristic p.

Provides explicit presentations for morphisms between p-Jones-Wenzl projectors.

Establishes a diagrammatic approach to understanding tilting modules in modular representation theory.

Abstract

Using diagrammatic methods, we define a quiver algebra depending on a prime p and show that it is the algebra underlying the category of tilting modules for SL(2) in characteristic p. Along the way we obtain a presentation for morphisms between p-Jones-Wenzl projectors.