Quantum Painleve systems and hypergeometric integrals

• Project/Area Number: 25887047
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Rikkyo University
• Principal Investigator: NAGOYA Hajime 立教大学, 理学部, 助教 (80447367)
• Project Period (FY): 2013-08-30 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000); Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 超幾何積分 / パンルヴェ系 / 共形場理論 / パンルヴェ方程式 / 量子パンルヴェ系 / モノドロミー保存変形

Outline of Final Research Achievements

Our aim was to establish an understanding of a relation between hypergeometric integrals and quantum Painleve systems. In this project, we constructed Schrodinger equations from hypergeometric integrals defined appropriately. Taking classical limit of those Schrodinger equations, we obtained Hamiltonian systems admitting hypergeometric integrals as special solutions. Our result give an understanding of a relation between hypergeometric integrals and Schrodinger systems.

Research Products

• [Journal Article] Fractional Calculus of quantum Painleve systems of type A_l^(1) (2015)
  • Author(s): Hajime Nagoya
  • Journal Title: Contemporary Mathematics Volume: 印刷中
  • Peer Reviewed
• [Presentation] Schrodinger systems from hypergeometric integrals I, II
  • Author(s): 名古屋 創
  • Organizer: Workshop on Accessory Parameters
  • Place of Presentation: 東京大学玉原国際セミナーハウス
• [Presentation] Schrodinger systems from hypergeometric integrals of Euler type
  • Author(s): 名古屋 創
  • Organizer: 2014 Joint Mathematics Meetings, AMS Special Session on Algebraic and Analytic Aspects of Integrable Systems and Painleve Equations
  • Place of Presentation: Baltimore Convention Center (USA)
  • Invited