Diagram categories for ${\text{U}}_q$-tilting modules at roots of unity

Henning Haahr Andersen, Daniel Tubbenhauer

We give a diagrammatic presentation of the category of ${\text{U}}_q({\mathfrak{sl}}_2)$-tilting modules $\mathfrak{T}$ for $q$ being a root of unity and introduce a grading on $\mat…