Quiver varieties and tensor products

  title={Quiver varieties and tensor products},
  author={Hiraku Nakajima},
  journal={Inventiones mathematicae},
  • H. Nakajima
  • Published 2 March 2001
  • Mathematics
  • Inventiones mathematicae
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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