g-vectors of Plücker Coordinates

Cluster algebras, introduced by Fomin and Zelevinsky, are commutative algebras characterised by intricate combinatorial structures and have applications across geometry and Lie theory, including examples such as Grassmannians, double Bruhat cells, and open Richardson varieties. In this talk, we will explore the Frobenius categorification of cluster algebras with coefficients. Using the additive categorification framework developed by Jensen--King--Su, we will explicitly determine the g-vectors of Plücker coordinates for the Grassmannian variety with respect to the triangular initial seed. This talk is based on a joint work with Bernhard Keller https://arxiv.org/pdf/2410.01037.