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Homological realization of Nakajima varieties and Weyl group actions

Published online by Cambridge University Press:  04 December 2007

Igor Frenkel ,
Mikhail Khovanov  and
Olivier Schiffmann
Igor Frenkel
Affiliation:
Department of Mathematics, Yale University, 10 Hillhouse Avenue, New Haven, CT 06520-8283, USA
Mikhail Khovanov
Affiliation:
Department of Mathematics, University of California, One Shields Avenue, Davis, CA 95616-8633, USAmikhail@math.ucdavis.edu
Olivier Schiffmann
Affiliation:
Department of Mathematics, Yale University, 10 Hillhouse Avenue, New Haven, CT 06520-8283, USA and DMA Ens Paris, 45 rue d'Ulm, 75005 Paris, Franceschiffma@dma.ens.fr
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Abstract

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We give a realization of Nakajima varieties and the action of the Weyl group on them using certain canonical structures of homological algebras and their natural generalization, which we develop in this paper. We consider in detail the case of an affine quiver, where we present a simple homological characterization of Nakajima varieties and its relation to moduli of sheaves on the projective plane.

Keywords

Nakajima quivers varietiesWeyl groupKoszul duality17B2016G2014D20
Type
Research Article
Information
Compositio Mathematica , Volume 141 , Issue 6 , November 2005 , pp. 1479 - 1503
Copyright
Foundation Compositio Mathematica 2005