Analysis of Infinite dimensional algebras and quantum field theories and their applications

• Project/Area Number: 17K05275
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Nagoya University
• Principal Investigator: Awata Hidetoshi 名古屋大学, 多元数理科学研究科, 准教授 (40314059)
• Project Period (FY): 2017-04-01 – 2022-03-31
• Project Status: Completed (Fiscal Year 2021)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: ディン・庵原・三木代数 / 量子トロイダル代数 / DAHA / 数理物理学 / 代数学 / 素粒子論 / 共形場理論

Outline of Final Research Achievements

We derived the generalization of the KZ equation associated with the Ding-Iohara-Miki (DIM) algebra and its R-matrix by using the braid and shift relations of the intertwiner of the DIM algebra. We constructed the intertwiner for a MacMahon representation and show that the intertwiners are permuted using the MacMahon R-matrix. We presented a candidate for the eigenfunction of the non-stationary Dell Hamiltonian.

Academic Significance and Societal Importance of the Research Achievements

ディン・庵原・三木(DIM)代数は、ホップ代数の構造と2つの中心を持つ無限次元代数であり、W無限大代数、(q-)ビラソロ代数や(q-)W代数などをその特殊な場合とし て内包している。又、我々が発見した様に、その相関関数は5次元超対称ヤンミルズ理論のネクラソフ分配関数と一致している。そのため最近非常に注目を集めている重要な代数である。

Research Products

• [Int'l Joint Research] Lebedev Physics Institute, Moscow/ITEP, Moscow/Inst. for Information Transmission Prob.(ロシア連邦)
• [Int'l Joint Research] Lebedev Physics Institute, Moscow/Inst. for Information Transmission Prob.(ロシア連邦)
• [Int'l Joint Research] Universit`a di Milano-Bicocca/INFN, sezione di Milano-Bicocca(イタリア)
• [Int'l Joint Research] ITEP, Moscow/Lebedev Physics Institute, Moscow/Inst. for Information Transmission Prob.(ロシア連邦)
• [Int'l Joint Research] Universit`a di Milano-Bicocca/INFN, sezione di Milano-Bicocca(イタリア)
• [Int'l Joint Research] ITEP, Moscow/Lebedev Physics Institute, Moscow/Inst. for Information Transmission Prob.(ロシア連邦)
• [Int'l Joint Research] Universit`a di Milano-Bicocca/INFN, sezione di Milano-Bicocca(イタリア)
• [Journal Article] On a complete solution of the quantum Dell system (2020)
  • Author(s): Awata Hidetoshi、Kanno Hiroaki、Mironov Andrei、Morozov Alexei
  • Journal Title: Journal of High Energy Physics Volume: 2020 Issue: 4 Pages: 212-212
  • DOI: 10.1007/jhep04(2020)212
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Shiraishi functor and non-Kerov deformation of Macdonald polynomials (2020)
  • Author(s): Awata Hidetoshi、Kanno Hiroaki、Mironov Andrei、Morozov Alexei
  • Journal Title: The European Physical Journal C Volume: 80 Issue: 10 Pages: 994-994
  • DOI: 10.1140/epjc/s10052-020-08540-4
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Elliptic lift of the Shiraishi function as a non-stationary double-elliptic function (2020)
  • Author(s): Awata Hidetoshi、Kanno Hiroaki、Mironov Andrei、Morozov Alexei
  • Journal Title: Journal of High Energy Physics Volume: 2020 Issue: 8 Pages: 150-150
  • DOI: 10.1007/jhep08(2020)150
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] The MacMahon R-matrix (2019)
  • Author(s): H.Awata, H.Kanno, A.Mironov, A.Morozov, K.Suetake and Y.Zenkevich
  • Journal Title: Journal of High Energy Physics Volume: 04 Issue: 4 Pages: 97-97
  • DOI: 10.1007/jhep04(2019)097
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Can tangle calculus be applicable to hyper polynomials? (2019)
  • Author(s): H. Awata, H. Kanno, A.Mironov, Al. Morozov
  • Journal Title: Nuclear Physics Volume: B949 Pages: 114816-114816
  • DOI: 10.1016/j.nuclphysb.2019.114816
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Nontorus link from topological vertex (2018)
  • Author(s): Awata Hidetoshi、Kanno Hiroaki、Mironov Andrei、Morozov Alexei、Morozov Andrey
  • Journal Title: Physical Review D Volume: 98 Issue: 4 Pages: 046018-046018
  • DOI: 10.1103/physrevd.98.046018
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] (q,t)-KZ Equations for quantum toroidal algebra and Nekrasov partition function on ALE spaces (2018)
  • Author(s): H.Awata, H.Kanno, A.Mironov, A.Morozov, K.Suetake and Y.Zenkevich
  • Journal Title: JHEP Volume: 1803 Issue: 3 Pages: 192-192
  • DOI: 10.1007/jhep03(2018)192
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Generalized Knizhnik-Zamolodchikov equation for Ding-Iohara-Miki algebra (2017)
  • Author(s): Awata Hidetoshi、Kanno Hiroaki、Mironov Andrei、Morozov Alexei、Morozov Andrey、Ohkubo Yusuke、Zenkevich Yegor
  • Journal Title: Physical Review D Volume: 96 Issue: 2 Pages: 026021-026021
  • DOI: 10.1103/physrevd.96.026021
  • Peer Reviewed / Int'l Joint Research
• [Presentation] 位相的頂点と丁・庵原・三木代数～菅野さんと歩んで17年～ (2020)
  • Author(s): Awata Hidetoshi
  • Organizer: Quantum Geometry in Gauge Theory and Strings, --多元数理ウェッビナー Kanno 60--, Nov. 21, 2020
  • Invited
• [Presentation] On DIM algebra and 5D AGT correspondence (2019)
  • Author(s): Awata Hidetoshi
  • Organizer: "Topological Field Theories, String theory and Matrix Models - 2019", August 26-31, 2019, ITEP
  • Int'l Joint Research / Invited
• [Presentation] Quantum Toroidal algebra gl1 and AGT correspondence (2019)
  • Author(s): Awata Hidetoshi
  • Organizer: "Workshop New Trends in Integrable Systems 2019", September 9-20, 2019, Osaka City Univ.
  • Int'l Joint Research / Invited
• [Presentation] On quantum toroidal algebras (2018)
  • Author(s): Awata Hidetoshi
  • Organizer: Workshop and School "Topological Field Theories, String theory and Matrix Models - 2018"
  • Int'l Joint Research / Invited
• [Presentation] On intertwiners of quantum toroidal $U_{q,d}(\widehat{\widehat{gl_N}})$ (2017)
  • Author(s): Hidetoshi Awata
  • Organizer: Workshop and School "Topological Field Theories, String theory and Matrix Models" Lebedev Physics Institute, Moscow, RUSSIA 2017, August, 25--31(August, 30)
• [Presentation] Ding-庵原-三木代数の表現論 (2017)
  • Author(s): Hidetoshi Awata
  • Organizer: 日本数学会秋季分科会特別講演, 山形大学, 2017年9月12日