Representation theoretical structure in massive integrable quantum field theories

• Project/Area Number: 20740088
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: University of Tsukuba
• Principal Investigator: TAKEYAMA Yoshiriro 筑波大学, 数理物質系, 准教授 (60375392)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 可積分系 / qKZ方程式 / 二重アフィンヘッケ代数 / 多重ゼータ値 / 量子可積分系 / アフィン2重ヘッケ代数

Research Abstract

We studied the rational quantum Knizhnik-Zamolodchikov (rational qKZ) equation, which is a difference equation playing an important role in the theory of massive integrable quantum field theories. We obtained special solutions and constructed a system of differential equations compatible with the rational qKZ equation by making use of representation theory of the double affine Hecke algebra. We also studied a q-analogue of the multiple zeta values and proved quadratic relations among them.

Research Products

• [Journal Article] Quadratic relations for a q-analogue of multiple zeta values (2011)
  • Author(s): Yoshihiro Takeyama
  • Journal Title: Ramanujan J. Volume: 27(1) Issue: 1 Pages: 15-18
  • DOI: 10.1007/s11139-011-9328-8
  • Peer Reviewed
• [Journal Article] Differential equations compatible with boundary rational qKZ equation, Proceedings of the Infinite Analysis 09-New Trends in Quantum Integrable Systems (2010)
  • Author(s): Yoshihiro Takeyama
  • Pages: 421-450
  • DOI: 10.1142/9789814324373_0021
  • Peer Reviewed
• [Journal Article] Differential equations compatible with boundary rational qKZ equation (2010)
  • Author(s): Yoshihiro Takeyama
  • Journal Title: Proceedings of the Infinite Analysis 09--New Trends in Quantum Integrable Systems Pages: 421-450
  • Peer Reviewed
• [Journal Article] A q-analogue of non-strict multiple zeta values and basic hypergeometric series (2009)
  • Author(s): Yoshihiro Takeyama
  • Journal Title: Proc. Amer. Math. Soc. Volume: 137(9) Issue: 09 Pages: 2997-3002
  • DOI: 10.1090/s0002-9939-09-09931-6
  • Peer Reviewed
• [Journal Article] The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials (2009)
  • Author(s): Saburo Kakei, Michitomo Nishizawa, Yoshihisa Saito, Yoshihiro Takeyama
  • Journal Title: SIGMA (Symmetry, Integrability, and Geometry. Methods and Applications. Electronic) Volume: 5
  • URL: http://dx.doi.org/10.3842/SIGMA.2009.010
  • Peer Reviewed
• [Journal Article] Hidden Grassmann Structure in the XXZ Model II : Creation Operators (2009)
  • Author(s): H. Boos, M. Jimbo, T. Miwa, F. Smirnov, Y. Takeyama
  • Journal Title: Commun. Math. Phys. Volume: 286(3) Issue: 3 Pages: 875-932
  • DOI: 10.1007/s00220-008-0617-z
  • Peer Reviewed
• [Journal Article] Hidden Grassmann structure in the XXZ model. II.Creation operators (2009)
  • Author(s): H.Boos, M.Jimbo, T.Miwa, F.Smirnov, Y.Takeyama
  • Journal Title: Communications in Mathematical Physics 286 Pages: 875-932
  • Peer Reviewed
• [Journal Article] The rational qKZ equation and shifted non-symmetric Jack polynomials (2009)
  • Author(s): S.Kakei, M.Nishizawa, Y.Saito, Y.Takeyama
  • Journal Title: SIGMA.Symmetry, Integrability and Geometry. Methods and Applications 5
  • Peer Reviewed
• [Journal Article] A q-analogue of non-strict multiple zeta values and basic hypergeometric series (2009)
  • Author(s): Yoshihiro Takeyama
  • Journal Title: Proceedings of the American Mathematical Society 137 Pages: 2997-3002
  • Peer Reviewed
• [Journal Article] A φ_<1,3>-filtration of the Virasoro minimal series M(p,p') with 1<p'/p<2 (2008)
  • Author(s): B. Feigin, E. Feigin, M. Jimbo, T. Miwa, Y. Takeyama
  • Journal Title: Publ. Res. Inst. Math. Sci. Volume: 44(2) Issue: 2 Pages: 213-257
  • DOI: 10.2977/prims/1210167327
  • Peer Reviewed
• [Journal Article] A φ_<1,3>-filtration of the Virasoro minimal series M(p, p') with 1<p/p'<2 (2008)
  • Author(s): B. Feigin, E. Feigin, M. Jimbo, T. Miwa, Y. Takeyama
  • Journal Title: Research Institute for Mathematical Sciences. Publications 44 Pages: 213-257
  • Peer Reviewed
• [Presentation] 多重ゼータ値のq類似が満たす2次関係式 (2011)
  • Author(s): 竹山美宏
  • Organizer: 日本数学会年会
  • Place of Presentation: 早稲田大学
  • Year and Date: 2011-03-22
• [Presentation] Differential equations compatible with boundary rational qKZ equation (2010)
  • Author(s): 竹山美宏
  • Organizer: 日本数学会年会
  • Place of Presentation: 慶應義塾大学
  • Year and Date: 2010-03-26
• [Presentation] The rational qKZ equation and shifted non-symmetric Jack polynomials (2009)
  • Author(s): 竹山美宏
  • Organizer: 日本数学会年会
  • Place of Presentation: 東京大学
  • Year and Date: 2009-03-29