--- _id: '9998' abstract: - lang: eng text: 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. 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).' article_number: '87' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Peter full_name: Koroteev, Peter last_name: Koroteev - first_name: Petr full_name: Pushkar, Petr id: 151DCEB6-9EC3-11E9-8480-ABECE5697425 last_name: Pushkar - first_name: Andrey V. full_name: Smirnov, Andrey V. last_name: Smirnov - first_name: Anton M. full_name: Zeitlin, Anton M. last_name: Zeitlin citation: ama: 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 apa: 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 chicago: 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. ieee: 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. ista: Koroteev P, Pushkar P, Smirnov AV, Zeitlin AM. 2021. Quantum K-theory of quiver varieties and many-body systems. Selecta Mathematica. 27(5), 87. mla: 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. short: P. Koroteev, P. Pushkar, A.V. Smirnov, A.M. Zeitlin, Selecta Mathematica 27 (2021). date_created: 2021-09-12T22:01:22Z date_published: 2021-08-30T00:00:00Z date_updated: 2023-08-14T06:34:14Z day: '30' ddc: - '530' department: - _id: TaHa doi: 10.1007/s00029-021-00698-3 external_id: isi: - '000692795200001' file: - access_level: open_access checksum: beadc5a722ffb48190e1e63ee2dbfee5 content_type: application/pdf creator: cchlebak date_created: 2021-09-13T11:31:34Z date_updated: 2021-09-13T11:31:34Z file_id: '10010' file_name: 2021_SelectaMath_Koroteev.pdf file_size: 584648 relation: main_file success: 1 file_date_updated: 2021-09-13T11:31:34Z has_accepted_license: '1' intvolume: ' 27' isi: 1 issue: '5' language: - iso: eng month: '08' oa: 1 oa_version: Published Version project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Selecta Mathematica publication_identifier: eissn: - 1420-9020 issn: - 1022-1824 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Quantum K-theory of quiver varieties and many-body systems tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 27 year: '2021' ...