---
DOAJ_listed: '1'
OA_place: publisher
OA_type: diamond
_id: '21718'
abstract:
- lang: eng
  text: "In this paper, we consider the big algebra recently introduced by Hausel
    for the GLn-action on the coordinate ring of the matrix space Mat(n,r). In particular,
    we obtain explicit formulas for the big algebra generators in terms of differential
    operators with polynomial coefficients. We show that big algebras in type A are
    commutative and relate them to the Bethe subalgebra in the Yangian Y(gln). We
    apply these results to big algebras of symmetric powers of the standard representation
    of GLn.\r\n."
acknowledgement: "I would like to express my gratitude to Tam´as Hausel for introducing
  me to the subject and\r\nfor his constant guidance throughout this work. I would
  also like to thank Tam´as Hausel,\r\nMischa Elkner, Jakub L¨owit, Anton Mellit,
  Marino Romero, Leonid Rybnikov for many fruitful\r\ndiscussions and feedback on
  earlier drafts of this paper. We are grateful to the anonymous\r\nreferees for many
  useful comments and suggestions that improved the manuscript. This work was done
  during the author’s PhD studies at the Institute of Science and Technology Austria
  (ISTA). The author was supported by the Austrian Science Fund (FWF) grant\r\n“Geometry
  of the tip of the global nilpotent cone” no. 10.55776/P35847 and the DOC Fellowship
  of the Austrian Academy of Sciences. The author also acknowledges the long-term
  program\r\nof support of the Ukrainian research teams at the Polish Academy of Sciences
  carried out in\r\ncollaboration with the U.S. National Academy of Sciences with
  the financial support of external\r\npartners. For open access purposes, the author
  has applied a CC BY public copyright license\r\nto any author-accepted manuscript
  version arising from this submission."
article_number: '024'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nhok T
  full_name: Ngo, Nhok T
  id: 28e53c8c-896a-11ed-bdf8-f809043ce2f0
  last_name: Ngo
citation:
  ama: 'Ngo NT. Big algebra in type A for the coordinate ring of the matrix space.
    <i>Symmetry, Integrability and Geometry: Methods and Applications</i>. 2026;22.
    doi:<a href="https://doi.org/10.3842/SIGMA.2026.024">10.3842/SIGMA.2026.024</a>'
  apa: 'Ngo, N. T. (2026). Big algebra in type A for the coordinate ring of the matrix
    space. <i>Symmetry, Integrability and Geometry: Methods and Applications</i>.
    National Academy of Science of Ukraine. <a href="https://doi.org/10.3842/SIGMA.2026.024">https://doi.org/10.3842/SIGMA.2026.024</a>'
  chicago: 'Ngo, Nhok T. “Big Algebra in Type A for the Coordinate Ring of the Matrix
    Space.” <i>Symmetry, Integrability and Geometry: Methods and Applications</i>.
    National Academy of Science of Ukraine, 2026. <a href="https://doi.org/10.3842/SIGMA.2026.024">https://doi.org/10.3842/SIGMA.2026.024</a>.'
  ieee: 'N. T. Ngo, “Big algebra in type A for the coordinate ring of the matrix space,”
    <i>Symmetry, Integrability and Geometry: Methods and Applications</i>, vol. 22.
    National Academy of Science of Ukraine, 2026.'
  ista: 'Ngo NT. 2026. Big algebra in type A for the coordinate ring of the matrix
    space. Symmetry, Integrability and Geometry: Methods and Applications. 22, 024.'
  mla: 'Ngo, Nhok T. “Big Algebra in Type A for the Coordinate Ring of the Matrix
    Space.” <i>Symmetry, Integrability and Geometry: Methods and Applications</i>,
    vol. 22, 024, National Academy of Science of Ukraine, 2026, doi:<a href="https://doi.org/10.3842/SIGMA.2026.024">10.3842/SIGMA.2026.024</a>.'
  short: 'N.T. Ngo, Symmetry, Integrability and Geometry: Methods and Applications
    22 (2026).'
corr_author: '1'
date_created: 2026-04-12T22:01:51Z
date_published: 2026-03-14T00:00:00Z
date_updated: 2026-04-16T06:11:12Z
day: '14'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.3842/SIGMA.2026.024
external_id:
  arxiv:
  - '2501.04605'
file:
- access_level: open_access
  checksum: 29b28b5f8717ed1a084a2b551d0fd284
  content_type: application/pdf
  creator: dernst
  date_created: 2026-04-16T06:06:54Z
  date_updated: 2026-04-16T06:06:54Z
  file_id: '21740'
  file_name: 2026_SIGMA_Ngo.pdf
  file_size: 975460
  relation: main_file
  success: 1
file_date_updated: 2026-04-16T06:06:54Z
has_accepted_license: '1'
intvolume: '        22'
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
project:
- _id: 34b2c9cb-11ca-11ed-8bc3-a50ba74ca4a3
  grant_number: P35847
  name: Geometry of the tip of the global nilpotent cone
- _id: e6c64f42-ab3c-11f0-94c7-a95658059ccc
  grant_number: '27483'
  name: Big algebras in classical types
publication: 'Symmetry, Integrability and Geometry: Methods and Applications'
publication_identifier:
  eissn:
  - 1815-0659
publication_status: published
publisher: National Academy of Science of Ukraine
quality_controlled: '1'
scopus_import: '1'
status: public
title: Big algebra in type A for the coordinate ring of the matrix space
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 22
year: '2026'
...