Algebras related to integrable systems

• Project/Area Number: 18740009
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Algebra
• Research Institution: Okayama University (2007-2008); Kyoto University (2006)
• Principal Investigator: SUZUKI Takeshi Okayama University, 大学院・自然科学研究科, 准教授 (30335294)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,600,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,000,000 (Direct Cost: ¥1,000,000); Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
• Keywords: Cherednik代数 / Hecke代数 / アフィンLie代数 / 量子群 / 共形場理論 / 最高ウエイト圏 / 最高ウエイト表現

Research Abstract

共形場理論とよばれる可解な場の理論の模型の代数的構造に注目し,そこに登場する代数系とその表現について研究を行った.結果,共形場理論の枠組みが,微分方程式系に関連して現れるCherednik代数と,系の対称性を記述するアフィンLie代数の表現の間の良い対応を与えていることがわかった.さらに,Cherednik代数の可積分な表現に関連して新たな組合せ論的対象が得られた.

Research Products

• [Journal Article] Double affine Hecke algebras, conformal coinvariants and Kostka polynomials (2006)
  • Author(s): Takeshi Suzuki
  • Journal Title: C.R. Acad. Sci. Paris. Ser. I, 343 Pages: 383-386
• [Journal Article] Double affine Hecke algebras, conformal coinvariants and Kostka poly-nomials (2006)
  • Author(s): Takeshi Suzuki
  • Journal Title: C.R.Acad.Sci.Paris Ser.I 343 Pages: 383-386
• [Presentation] "Conformal field theory and Cherednik algebras" (2009)
  • Author(s): 鈴木武史
  • Organizer: Algebraic Lie structures with origins in physics
  • Place of Presentation: ケンブリッジ(イギリス)
  • Year and Date: 2009-03-24
• [Presentation] Conformal Field Theory and Cherednik Algebras (2009)
  • Author(s): 鈴木武史
  • Organizer: Algebraic Lie Structures with Origins in Physics
  • Place of Presentation: Cambridge大学Newton研
  • Year and Date: 2009-03-24
• [Presentation] Cylindric combinatorics and the representation theory of Cherednik algebras (2008)
  • Author(s): 鈴木武史
  • Organizer: 名古屋国際コンファレンス"Combinatorics and representation theory"
  • Place of Presentation: 名古屋
  • Year and Date: 2008-09-01
• [Presentation] Cylindrical combinatorics and the representation theory of Cherednik algebras of type A (2007)
  • Author(s): 鈴木武史
  • Organizer: 国際研究集会 "Cherednik Algebras"
  • Place of Presentation: エジンバラ(イギリス)
  • Year and Date: 2007-06-19
• [Presentation] Cylindrical combinatorics and the representation theory of Cherednik algebras (2007)
  • Author(s): 鈴木武史
  • Organizer: Cherednik Algebrasa
  • Place of Presentation: エジンバラ大学
  • Year and Date: 2007-06-19
• [Presentation] "Conformal field theory and double affine Hecke algebras"名古屋国際コンファレンス (2006)
  • Author(s): 鈴木武史
  • Organizer: Representation Theory of Algebraic Groups and Quantum Groups 06
  • Place of Presentation: 名古屋
  • Year and Date: 2006-06-16