福井大学 研究者総覧
工学系部門
工学領域
物理工学講座
更新日:2025/04/28
准教授
マツモト タクヤ
松本 拓也

福井大学 工学系部門 工学領域 物理工学講座 准教授

学位

  1. 2010/03/25数理学Nagoya university

論文

  1. Drinfeld realization of the centrally extended psl(2|2) Yangian algebra with the manifest coproducts2023/04/27Takuya Matsumoto・arXiv への公開(2022/08/26時点)。 ・Journal of Mathematical Physics (JMP) に2022/09/05に投稿、2023/04/07に受理(accept)。 ・2023/04/27に出版(Published Online)。 Cite as: J. Math. Phys. 64, 041704 (2023); doi: 10.1063/5.0124333 Submitted: 5 September 2022 • Accepted: 7 April 2023 • Published Online: 27 April 202310.48550/arXiv.2208.11889URLThe Lie superalgebra psl(2|2) is recognized as a pretty special one in both mathematics and theoretical physics. In this paper, we present the Drinfeld realization of the Yangian algebra associated with the centrally extended Lie superalgebra psl(2|2). Furthermore, we show that it possesses the Hopf algebra structures, particularly the coproducts. The idea to prove the existence of the manifest coproducts is the following. Firstly, we shall introduce them to Levendorskii's realization, a system of a finite truncation of the Drinfeld generators. Secondly, we show that Levendorskii's realization is isomorphic to the Drinfeld realization by induction.
  2. Free field realizations of the Virasoro primary fields of the extended W-algebras of type A1 at positive rational levels2022/04/14Takuya MatsumotoToyama Math. J. Vol. 42(2021), 89-136Vol. 42(2021), 89-136機関リポジトリ
  3. Explicit examples of the nilpotency of the Virasoro screening operators2022/04/01Takuya MatsumotoProceedings of Summer Seminar on Lie Algebras and Related Topics 36 (2021)

講演・口頭発表・ポスター等

  1. Drinfeld realization of the centrally extended psl(2|2) Yangian algebra with the manifest coproducts大阪公立大学 セミナー2023/03/06The Lie superalgebra psl(2|2) is recognized as a pretty special one in both mathematics and theoretical physics. In this talk, I will propose the Drinfeld realization of the Yangian algebra associated with the centrally extended Lie superalgebra psl(2|2). Furthermore, I show that it possesses the Hopf algebra structures, particularly the coproducts. The idea to prove the existence of the manifest coproducts is the following. Firstly, I shall introduce them to Levendorskii's realization, a system of a finite truncation of the Drinfeld generators. Secondly, I show that the Levendorskii's realization is isomorphic to the Drinfeld realization by induction. If time allows, I would like to mention the related topics and some future directions. This talk is mainly based on the preprint [arXiv:2208.11889 [math.QA]].
  2. 回転する円板の幾何学的位相について第93回形の科学シンポジウム「知識社会における形」2022/11/21The notion of the geometric phase is ubiquitous in physics. It could be understood as the physical realization of the holonomy in differential geometry. This talk addresses a very primitive toy model, a rotating disk around another fixed disc. We show that the rotation angle of the rotating disc manifestly exhibits the geometric phase.
  3. Drinfeld realization of the centrally extended psl(2|2) Yangian algebra with the manifest coproductsETH Zurich, Seminar series ”QFT, Strings & Beyond”2022/10/06The Lie superalgebra psl(2|2) is recognized as a pretty special one in both mathematics and theoretical physics. In this talk, I will propose the Drinfeld realization of the Yangian algebra associated with the centrally extended Lie superalgebra psl(2|2). Furthermore, I show that it possesses the Hopf algebra structures, particularly the coproducts. The idea to prove the existence of the manifest coproducts is the following. Firstly, I shall introduce them to Levendorskii's realization, a system of a finite truncation of the Drinfeld generators. Secondly, I show that Levendorskii's realization is isomorphic to the Drinfeld realization by induction. If time allows, I would like to mention the related topics and some future directions. This work is based on the preprint [arXiv:2208.11889 [math.QA]].
  4. Drinfeld realization of the centrally extended psl(2|2) Yangian algebra with the manifest coproducts多弦数理物理学セミナー(名古屋大学多元数理科学研究科におけるセミナー発表)2022/09/13
  5. Towards BGG resolutions for the affine Lie superalgebra sl(2|2)第37回 リー代数サマーセミナー2022/08/27

科学研究費補助金・厚生科研補助金

  1. 2024日本学術振興会科学研究費助成事業2次元共形場理論におけるスクリーニング作用素の複眼的探求基盤研究(C)(一般)
  2. 2022日本学術振興会科学研究費助成事業スーパー量子群がつなぐ2次元共形場理論と1次元ハバード模型基盤研究(C)
  3. 2021日本学術振興会科学研究費助成事業スーパー量子群がつなぐ2次元共形場理論と1次元ハバード模型基盤研究(C)