# 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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