# Quiver varieties and tensor products

@article{Nakajima2001QuiverVA, title={Quiver varieties and tensor products}, author={Hiraku Nakajima}, journal={Inventiones mathematicae}, year={2001}, volume={146}, pages={399-449} }

Abstract.In this article, we give geometric constructions of tensor products in various categories using quiver varieties. More precisely, we introduce a lagrangian subvariety &?tilde; in a quiver variety, and show the following results: (1) The homology group of &?tilde; is a representation of a symmetric Kac-Moody Lie algebra ?, isomorphic to the tensor product V(λ1)⊗...⊗V(λN) of integrable highest weight modules. (2) The set of irreducible components of &?tilde; has a structure of a crystal…

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