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Journal of the American Mathematical Society

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ISSN 1088-6834 (online) ISSN 0894-0347 (print)

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Elliptic stable envelopes
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by Mina Aganagic and Andrei Okounkov
J. Amer. Math. Soc. 34 (2021), 79-133
Published electronically: December 9, 2020


We construct stable envelopes in equivariant elliptic cohomology of Nakajima quiver varieties. In particular, this gives an elliptic generalization of the results of Maulik and Okounkov [Astérisque 408 (2019), ix+209]. We apply them to the computation of the monodromy of $q$-difference equations arising in the enumerative K-theory of rational curves in Nakajima varieties, including the quantum Knizhnik–Zamolodchikov equations.
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Bibliographic Information
  • Mina Aganagic
  • Affiliation: Department of Mathematics, University of California, Berkeley, 970 Evans Hall, Berkeley, California 94720
  • MR Author ID: 616605
  • ORCID: 0000-0001-8547-494X
  • Andrei Okounkov
  • Affiliation: Higher School of Economics, Columbia University, 420 West 118th Street, New York, New York 10027
  • MR Author ID: 351622
  • Email:
  • Received by editor(s): April 28, 2016
  • Received by editor(s) in revised form: November 24, 2018, November 21, 2019, February 18, 2020, and March 10, 2020
  • Published electronically: December 9, 2020
  • Additional Notes: The first author was supported, in part, by the NSF grant #1521446.
    The second author thanks the Simons foundation for being financially supported as a Simons investigator and the NSF for supporting enumerative geometry at Columbia as a part of FRG 1159416.

  • Dedicated: To Igor Krichever, with gratitude for inspiration and friendship
  • © Copyright 2020 by the authors
  • Journal: J. Amer. Math. Soc. 34 (2021), 79-133
  • MSC (2010): Primary 22E99
  • DOI:
  • MathSciNet review: 4188815