Séminaire Lotharingien de Combinatoire, 85B.83 (2021), 12 pp.
Volker Genz and Gleb Koshevoy
Maximal Green Sequences for Triangle Products
Abstract.
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.
Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.
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