Quiver varieties and cluster algebras

We realize a Fomin-Zelevinsky cluster algebra as a subquotient of the dual of the upper part of the quantized enveloping algebra. Then we show that Lusztig dual canonical base induces a base of the cluster algebra which includes all the cluster monomials. In particular, the positivity conjecture on cluster monomials is a simple consequence.

nakajima@math.kyoto-u.ac.jp