Semicanonical bases and preprojective algebras II: A multiplication formula

@article{Geiss2007SemicanonicalBA,
  title={Semicanonical bases and preprojective algebras II: A multiplication formula},
  author={Christof Geiss and Bernard Leclerc and Jan Schroer},
  journal={Compositio Mathematica},
  year={2007},
  volume={143},
  pages={1313 - 1334}
}
Let $\mathfrak{n}$ be a maximal nilpotent subalgebra of a complex symmetric Kac–Moody Lie algebra. Lusztig has introduced a basis of $U(\mathfrak{n})$ 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 $\mathfrak{n}$. 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… 
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