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Elliptic stable envelopes


Authors: Mina Aganagic and Andrei Okounkov
Journal: J. Amer. Math. Soc. 34 (2021), 79-133
MSC (2010): Primary 22E99
DOI: https://doi.org/10.1090/jams/954
Published electronically: December 9, 2020
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Abstract: 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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Additional Information

Mina Aganagic
Affiliation: Department of Mathematics, University of California, Berkeley, 970 Evans Hall, Berkeley, California 94720

Andrei Okounkov
Affiliation: Higher School of Economics, Columbia University, 420 West 118th Street, New York, New York 10027
Email: okounkov@math.columbia.edu

DOI: https://doi.org/10.1090/jams/954
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
Article copyright: © Copyright 2020 by the authors