Quantum integrable system of type <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mi>A</mi></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/9E5D72D2-707A-40be-A820-129A7FC6C3C0-M002.jpg"><?fx-imagestate width="3.04800010" height="3.47133350"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/9E5D72D2-707A-40be-A820-129A7FC6C3C0-M002c.jpg"><?fx-imagestate width="3.04800010" height="3.47133350"?></graphic></alternatives></inline-formula> minimal nilpotent orbit

YU Sirui; HE Weiqiang

doi:10.13471/j.cnki.acta.snus.ZR20250002

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Quantum integrable system of type

A

minimal nilpotent orbit

Research articles | 更新时间：2025-11-14

- Quantum integrable system of type $A$ minimal nilpotent orbit
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 64, Issue 3, Pages: 165-172(2025)
- 作者机构：
  
  中山大学数学学院，广东广州 510275
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20250002
  CLC： O187
- Received：02 January 2025，
  
  Accepted：22 February 2025，
  
  Published Online：07 May 2025，
  
  Published：25 May 2025
- 稿件说明：
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余思睿,何伟强.A型极小幂零轨道的量子可积系统[J].中山大学学报(自然科学版)(中英文),2025,64(03):165-172.

YU Sirui,HE Weiqiang.Quantum integrable system of type A minimal nilpotent orbit[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(03):165-172.
余思睿,何伟强.A型极小幂零轨道的量子可积系统[J].中山大学学报(自然科学版)(中英文),2025,64(03):165-172. DOI： 10.13471/j.cnki.acta.snus.ZR20250002.

YU Sirui,HE Weiqiang.Quantum integrable system of type A minimal nilpotent orbit[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(03):165-172. DOI： 10.13471/j.cnki.acta.snus.ZR20250002.

Quantum integrable system of type

A

minimal nilpotent orbit

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摘要

研究了

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2.28600001

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497265&type=

1.94733346

型极小幂零轨道的量子可积系统，证明了

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3.21733332

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2.96333337

极小轨道的经典可积系统中的Hamilton量的量子化是

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497304&type=

3.21733332

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2.96333337

极小轨道的量子可积系统.

Abstract

We study the quantum integrable system of type

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2.62466669

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497292&type=

2.28600001

minimal nilpotent orbit and prove that the quantization of the Hamiltonian in classical integrable system of

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3.72533321

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497314&type=

3.47133350

minimal nilpotent orbit is the quantum integrable system of

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3.72533321

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82497315&type=

3.47133350

minimal nilpotent orbit.

关键词

Keywords

references

BOURBAKI N ， 2002 . Lie groups and Lie algebras： Chapters 4-6 ［M］. Berlin ： Springer .

BRADEN T ， LICATA A ， PROUDFOOT N ， et al ， 2016 . Quantizations of conical symplectic resolutions II： Category <math id="M400"><mi mathvariant="italic">𝒪</mi></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82498627&type= 2.70933342 https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82498639&type= 3.04800010 and symplectic duality ［J］. Astérisque ， 384 ： 75 - 179 .

BRADEN T ， PROUDFOOT N ， WEBSTER B ， 2016 . Quantizations of conical symplectic resolutions I： Local and global structure ［J］. Astérisque ， 384 ： 1 - 73 .

BRAVERMAN A ， FINKELBERG M ， NAKAJIMA H ， 2019 . Coulomb branches of 3d <math id="M401"><mi mathvariant="normal">𝒩</mi><mo>=</mo><mn mathvariant="normal">4</mn></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82498655&type= 3.13266683 https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82498668&type= 9.56733322 quiver gauge theories and slices in the affine Grassmannian ［J］. Adv Theor Math Phys ， 23 （ 1 ）： 75 - 166 .

BULLIMORE M ， DIMOFTE T ， GAIOTTO D ， et al ， 2016 . Boundaries， mirror symmetry， and symplectic duality in 3d <math id="M402"><mi mathvariant="normal">𝒩</mi><mo>=</mo><mn mathvariant="normal">4</mn></math> https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82498655&type= 3.13266683 https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=82498668&type= 9.56733322 gauge theory ［J］. J High Energy Phys ， 2016 （ 10 ）： 108 .

CHEN X J ， HE W Q ， YU S R ， 2023 . Quantization of the minimal nilpotent orbits and the quantum Hikita conjecture ［EB/OL］. arXiv ： 2302 . 13249 . https：//arxiv.org/abs/2302.13249v4 https://arxiv.org/abs/2302.13249v4 .

GARFINKLE D ， 1982 . A new construction of the Joseph ideal ［D］. Cambridge ： Massachusetts Institute of Technology .

JOSEPH A ， 1976 . The minimal orbit in a simple Lie algebra and its associated maximal ideal ［J］. Ann Sci École Norm Sup ， 9 （ 1 ）： 1 - 29 .

LOSEV I ， 2012 . Isomorphisms of quantizations via quantization of resolutions ［J］. Adv Math ， 231 （ 3/4 ）： 1216 - 1270 .

MALKIN A ， OSTRIK V ， VYBORNOV M ， 2005 . The minimal degeneration singularities in the affine Grassmannians ［J］. Duke Math J ， 126 （ 2 ）： 233 - 249 .

TU X ， 2024 . Integrable system on minimal nilpotent orbit ［EB/OL］. arXiv ： 2408 . 13020 . https：//arxiv.org/abs/2408.13020v2 https://arxiv.org/abs/2408.13020v2 .

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Quantum integrable system of type A minimal nilpotent orbit

DOI：10.13471/j.cnki.acta.snus.ZR20250002

摘要

Abstract

关键词

Keywords

references

Quantum integrable system of type $A$ minimal nilpotent orbit