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Coherent sheaves on quiver varieties and categorification

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Abstract

We construct geometric categorical \(\mathfrak g \) actions on the derived category of coherent sheaves on Nakajima quiver varieties. These actions categorify Nakajima’s construction of Kac–Moody algebra representations on the K-theory of quiver varieties. We define an induced affine braid group action on these derived categories.

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Notes

  1. Here we are using the Krull–Schmidt property of our categories. For more details, see [5], section 4.1.

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Acknowledgments

We would like to thank Roman Bezrukavnikov, Alexander Braverman, Christopher Dodd, Hiraku Nakajima, and Raphael Rouquier for helpful discussions. S.C. was supported by NSF Grant 0801939/0964439 and J.K. by NSERC. A.L. would also like to thank the Max Planck Institute in Bonn for support during the 2008–2009 academic year.

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Authors and Affiliations

  1. Department of Mathematics, University of Southern California, Los Angeles, CA, USA

    Sabin Cautis

  2. Department of Mathematics, University of Toronto, Toronto, ON, USA

    Joel Kamnitzer

  3. Department of Mathematics, Stanford University, Palo Alto, CA, USA

    Anthony Licata

Authors
  1. Sabin Cautis
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  2. Joel Kamnitzer
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  3. Anthony Licata
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Correspondence to Joel Kamnitzer.

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Cautis, S., Kamnitzer, J. & Licata, A. Coherent sheaves on quiver varieties and categorification. Math. Ann. 357, 805–854 (2013). https://doi.org/10.1007/s00208-013-0921-6

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  • DOI: https://doi.org/10.1007/s00208-013-0921-6

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