---
_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. <i>Selecta Mathematica</i>. 2021;27(5). doi:<a href="https://doi.org/10.1007/s00029-021-00698-3">10.1007/s00029-021-00698-3</a>
  apa: Koroteev, P., Pushkar, P., Smirnov, A. V., &#38; Zeitlin, A. M. (2021). Quantum
    K-theory of quiver varieties and many-body systems. <i>Selecta Mathematica</i>.
    Springer Nature. <a href="https://doi.org/10.1007/s00029-021-00698-3">https://doi.org/10.1007/s00029-021-00698-3</a>
  chicago: Koroteev, Peter, Petr Pushkar, Andrey V. Smirnov, and Anton M. Zeitlin.
    “Quantum K-Theory of Quiver Varieties and Many-Body Systems.” <i>Selecta Mathematica</i>.
    Springer Nature, 2021. <a href="https://doi.org/10.1007/s00029-021-00698-3">https://doi.org/10.1007/s00029-021-00698-3</a>.
  ieee: P. Koroteev, P. Pushkar, A. V. Smirnov, and A. M. Zeitlin, “Quantum K-theory
    of quiver varieties and many-body systems,” <i>Selecta Mathematica</i>, 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.” <i>Selecta Mathematica</i>, vol. 27, no. 5, 87, Springer Nature, 2021,
    doi:<a href="https://doi.org/10.1007/s00029-021-00698-3">10.1007/s00029-021-00698-3</a>.
  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'
...