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Mathematische Zeitschrift

, Volume 292, Issue 1–2, pp 611–639 | Cite as

A categorical action on quantized quiver varieties

  • Ben WebsterEmail author
Article
  • 52 Downloads

Abstract

In this paper, we describe a categorical action of any symmetric Kac–Moody algebra on a category of quantized coherent sheaves on Nakajima quiver varieties. By “quantized coherent sheaves,” we mean a category of sheaves of modules over a deformation quantization of the natural symplectic structure on quiver varieties. This action is a direct categorification of the geometric construction of universal enveloping algebras by Nakajima.

Notes

Acknowledgements

This paper owes a great debt to Yiqiang Li; his work was an important inspiration, and he very helpfully pointed out a serious mistake in a draft version. The paper also benefited from many helpful comments by an anonymous referee. I also want to thank Nick Proudfoot, Tony Licata and Tom Braden; I depended very much on previous work and conversations with them to be able to write this paper. I thank Sabin Cautis and Aaron Lauda for sharing an early version of their paper with me. I also appreciate very stimulating conversations with Catharina Stroppel, Ivan Losev and Peter Tingley.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Pure MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Perimeter Institute for Mathematical PhysicsWaterlooCanada

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