Generic bases for cluster algebras and the Chamber Ansatz

Understand

Let Q be a finite quiver without oriented cycles, and let $\Lambda$ be the corresponding preprojective algebra.

• Let g be the Kac-Moody Lie algebra with Cartan datum given by Q, and let W be its Weyl group.
• With w in W is associated a unipotent cell N^w of the Kac-Moody group with Lie algebra g.
• In previous work we proved that the coordinate ring \C[N^w] of N^w is a cluster algebra in a natural way.