Real Roots in the Root System T2,p,q

Motivated by the recent advances in the categorification of the cluster structure on the coordinate rings of Grassmannians of k-subspaces in n-space, we investigate a particular construction of root systems of type T2,p,q, including the type En. This construction generalizes Manin's "hyperbolic construction" of E8 and reveals a lot of otherwise hidden regularities in this family of root systems.