  Let $n$ be a maximal nilpotent subalgebra of a complex symmetric Kac-Moody
Lie algebra. Lusztig has introduced a basis of U(n) called the semicanonical
basis, whose elements can be seen as certain constructible functions on
varieties of nilpotent modules over a preprojective algebra of the same type as
$n$. We prove a formula for the product of two elements of the dual of this
semicanonical basis, and more generally for the product of two evaluation forms
associated to arbitrary modules over the preprojective algebra. This formula
plays an important role in our work on the relationship between semicanonical
bases, representation theory of preprojective algebras, and Fomin and
Zelevinsky's theory of cluster algebras. It was inspired by recent results of
Caldero and Keller.
