Study of Integrable Systems by the Method of Algebraic Analysis

• Project/Area Number: 22340031
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Kyoto University
• Principal Investigator: MIWA tetsuji 京都大学, 学内共同利用施設等, 教授 (10027386)
• Project Period (FY): 2010-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000); Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2010: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
• Keywords: 量子トロイダル代数 / 可解格子模型 / スピン鎖 / 相関函数 / 平面分割 / フェルミオン / 最高ウエイト表現 / 頂点模型 / 量子可積分系 / サインゴルドン模型 / 形状因子 / 局所場 / 積分表示 / 半無限積 / 共形場理論

Research Abstract

Fermionic construction of creation operators is extended to the sine-Gordon model. The fermion creation operator in this approach was identified with the BBS fermion in the study of form factors. We alsostudied the quantum tproidal algebra.

Research Products

• [Journal Article] Representations of quantum toroidal gln (2013)
  • Author(s): Feigin, Boris;Jimbo, Michio;Miwa, Tetsuji;Mukhin, Evgheny
  • Journal Title: Jornal of Algebra Volume: 380 Pages: 78-108
  • DOI: 10.1016/j.jalgebra.2012.12.029
  • Peer Reviewed
• [Journal Article] Fermions Acting on Quasi-local Operators in the XXZ Model (2013)
  • Author(s): Michio Jimbo, Tetsuji Miwa, and Feodor Smirnov
  • Journal Title: Springer Proceedings in Mathematics & Statistics Volume: 40 Pages: 243-261
  • DOI: 10.1007/978-1-4471-4863-0_10
  • ISBN: 9781447148623, 9781447148630
  • Peer Reviewed
• [Journal Article] Quantum toroidal gl(1) algebra : plane partitions (2012)
  • Author(s): Feigin B, Jimbo M, Miwa T, Mukhin E
  • Journal Title: Kyoto J. Math Volume: 52 Pages: 621-659
• [Journal Article] Quantum toroidal gl1-algebra: plane partitions (2012)
  • Author(s): Boris Feigin
  • Journal Title: Kyoto J. Math. Volume: 52 Issue: 3 Pages: 621-659
  • DOI: 10.1215/21562261-1625217
• [Journal Article] Gelfand Zetlin basis, Whittacker vectors and a bosonic formula for the sl(n+1) principal subspace (2011)
  • Author(s): Feigin B, Jimbo M, Miwa T
  • Journal Title: Publ. Res. Inst. Math Volume: 47 Pages: 535-551
• [Journal Article] Fermionic structure in the sine Gordon model : form factor and null vectors (2011)
  • Author(s): Jimbo M, Miwa T, Smirnov F
  • Journal Title: Nuclear Physics Volume: B.852 Pages: 390-440
• [Journal Article] Quantum continuous gl(n) : tensor products of Fock modules and Wn charac- ters (2011)
  • Author(s): Feigin B, Jimbo M, Miwa T, Mukhin E
  • Journal Title: Kyoto J. Math Volume: 51 Pages: 237-364
• [Journal Article] Hidden Grassmann structure in the XXZ model V, sine-Gordon model (2011)
  • Author(s): Jimbo M, Miwa T, SmirnovF
  • Journal Title: Lett. Math. Phys Volume: 96 Pages: 325-365
• [Journal Article] Gelfand-Zetlin basis, Whittaker vectors and a bosonic formula for the sln+1 principal subspace (2011)
  • Author(s): Feigin, B.; Jimbo, M.; Miwa, T
  • Journal Title: Publ.Res.Inst.Math. Volume: 47 Issue: 2 Pages: 535-551
  • DOI: 10.2977/prims/42
  • Peer Reviewed
• [Journal Article] Fermionic structure in the sine-Gordon model : form factors and null-vectors (2011)
  • Author(s): Jimbo, M.; Miwa, T.; Smirnov, F
  • Journal Title: Nuclear Phys.B Volume: 852 Issue: 2 Pages: 390-440
  • DOI: 10.1016/j.nuclphysb.2011.06.016
  • Peer Reviewed
• [Journal Article] Quantum continuous gl∞ : tensor products of Fock modules and Wn-characters (2011)
  • Author(s): Feigin, B.; Feigin, E.; Jimbo, M.; Miwa, T.; Mukhin, E.
  • Journal Title: Kyoto J.Math. Volume: 51 Issue: 2 Pages: 237-364
  • DOI: 10.1016/j.aim.2004.04.009
  • Peer Reviewed
• [Journal Article] Hidden Grassmann structure in the XXZ model IV : CFT limit (2010)
  • Author(s): Boos H, Jimbo M, Miwa T, Smirnov F
  • Journal Title: Comm. Math. Phys Volume: 299(3) Pages: 825-866
• [Journal Article] Hidden Grassmann structure in the XXZ model IV : CFT limit. (2010)
  • Author(s): Boos, H., Jimbo, M., Miwa, T., Smirnov, F.
  • Journal Title: Comm.Math.Phys. Volume: 299, no.3 Pages: 825-866
• [Journal Article] Fermionic screening operators in the sine-Gordon model
  • Author(s): Jimbo M, Miwa T, SmirnovF
  • Volume: arxiv1103.1534
• [Journal Article] Creation operators for the Fateev-Zamolodvhikov spin chain
  • Author(s): Jimbo M, Miwa T, SmirnovF
• [Journal Article] Branching rules for quantum toroidal gl(n)
  • Author(s): Feigin,B.,Jimbo,M., Miwa, T., Mukhin
• [Presentation] Construction of creation operators i n Fateev-Zamolodchikov model, mathematical Physics : Past, Present, and Future (2014)
  • Organizer: Euler Institute in St.Petersburg
  • Place of Presentation: Russia
• [Presentation] Correlation functions in Integrable models, in Representation Theory ans applications to Combinatorics, Geometry, and Quantum Physics (2013)
  • Organizer: International Conference dedicated to the 60th birthday of Boris Feigin
  • Place of Presentation: Moscow
• [Presentation] Representations of quantum continuous glinfinity (2010)
  • Organizer: ICM satellite conference on Algebraic and Combinatorial approach in representation theory
  • Place of Presentation: Bangalore, India
  • Year and Date: 2010-08-15
• [Presentation] Representations of quantum continuous gl infinity (2010)
  • Author(s): 三輪哲二
  • Organizer: ICM satellite conference on Algebraic and Combinatorial approaches to representation theory
  • Place of Presentation: Bangalore, India(招待講演)
  • Year and Date: 2010-08-15
• [Presentation] Heinemann賞の受賞講演
  • Organizer: アメリカ物理学会年会
  • Place of Presentation: Baltimore