| Résume | The existence of maximal green sequences is an important property of a cluster algebra. We construct explicit maximal green sequences for triangle products of an acylic quiver with a Dynkin quiver. As an application we deduce from the work of Gross-Hacking-Keel-Kontsevich the full Fock-Goncharov conjecture for big double Bruhat cells for simply-connected, connected, semisimple groups of simply-laced type. Maximal green sequences are also useful for computing Donaldson-Thomas invariants and transformations. We compute normalized DT-invariants for triangle products of Dynkin quivers. For products of the Dynkin quivers, the DT-transformations are related to the Robinson-Schensted-Knuth bijection. The talk is based on joint work with V.Genz and work in progress with T.Scrimshaw. |
