Quantum K-theory of quiver varieties and many-body systems

Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. 2021. Quantum K-theory of quiver varieties and many-body systems. Selecta Mathematica. 27(5), 87.

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Author
Koroteev, Peter; Pushkar, PetrIST Austria; Smirnov, Andrey V.; Zeitlin, Anton M.
Department
Abstract
We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic version of results of Givental and Kim, connecting quantum geometry of flag varieties and Toda lattice.
Publishing Year
Date Published
2021-08-30
Journal Title
Selecta Mathematica
Acknowledgement
First of all we would like to thank Andrei Okounkov for invaluable discussions, advises and sharing with us his fantastic viewpoint on modern quantum geometry. We are also grateful to D. Korb and Z. Zhou for their interest and comments. The work of A. Smirnov was supported in part by RFBR Grants under Numbers 15-02-04175 and 15-01-04217 and in part by NSF Grant DMS–2054527. The work of P. Koroteev, A.M. Zeitlin and A. Smirnov is supported in part by AMS Simons travel Grant. A. M. Zeitlin is partially supported by Simons Collaboration Grant, Award ID: 578501. Open access funding provided by Institute of Science and Technology (IST Austria).
Volume
27
Issue
5
Article Number
87
ISSN
eISSN
IST-REx-ID

Cite this

Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. Quantum K-theory of quiver varieties and many-body systems. Selecta Mathematica. 2021;27(5). doi:10.1007/s00029-021-00698-3
Koroteev, P., Pushkar, P., Smirnov, A. V., & Zeitlin, A. M. (2021). Quantum K-theory of quiver varieties and many-body systems. Selecta Mathematica. Springer Nature. https://doi.org/10.1007/s00029-021-00698-3
Koroteev, Peter, Petr Pushkar, Andrey V. Smirnov, and Anton M. Zeitlin. “Quantum K-Theory of Quiver Varieties and Many-Body Systems.” Selecta Mathematica. Springer Nature, 2021. https://doi.org/10.1007/s00029-021-00698-3.
P. Koroteev, P. Pushkar, A. V. Smirnov, and A. M. Zeitlin, “Quantum K-theory of quiver varieties and many-body systems,” Selecta Mathematica, vol. 27, no. 5. Springer Nature, 2021.
Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. 2021. Quantum K-theory of quiver varieties and many-body systems. Selecta Mathematica. 27(5), 87.
Koroteev, Peter, et al. “Quantum K-Theory of Quiver Varieties and Many-Body Systems.” Selecta Mathematica, vol. 27, no. 5, 87, Springer Nature, 2021, doi:10.1007/s00029-021-00698-3.
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