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A study of commutative rings of differential operators in completely integrable models and their eigenfunctions

Research Project

Project/Area Number 17340046
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionOsaka University

Principal Investigator

DATE Etsuro  Osaka University, 大学院・情報科学研究科, 教授 (00107062)

Co-Investigator(Kenkyū-buntansha) 川中 宣明  大阪大学, 大学院・情報科学研究科, 教授 (10028219)
松村 昭孝  大阪大学, 大学院・情報科学研究科, 教授 (60115938)
小松 玄  大阪大学, 大学院・理学研究科, 准教授 (60108446)
三木 敬  大阪大学, 大学院・情報科学研究科, 准教授 (40212229)
山根 宏之  大阪大学, 大学院・情報科学研究科, 准教授 (10230517)
尾角 正人  大阪大学, 大学院・基礎工学研究科, 助教授 (70221843)
野海 正俊  神戸大学, 大学院・自然科学研究科, 教授 (80164672)
Co-Investigator(Renkei-kenkyūsha) KAWANAKA Noriaki  大阪大学, 大学院・情報科学研究科, 教授 (10028219)
MATSUMURA Akitaka  大阪大学, 大学院・情報科学研究科, 教授 (60115938)
KOMATSU Gen  大阪大学, 大学院・理学研究科, 准教授 (60108446)
MIKI Kei  大阪大学, 大学院・情報科学研究科, 准教授 (40212229)
YAMANE Hiroyuki  大阪大学, 大学院・情報科学研究科, 准教授 (10230517)
OKADO Masato  大阪大学, 大学院・基礎工学研究科, 准教授 (70221843)
NOUMI Masatoshi  神戸大学, 大学院・理学研究科, 教授 (80164672)
Project Period (FY) 2005 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥8,700,000 (Direct Cost: ¥7,800,000、Indirect Cost: ¥900,000)
Fiscal Year 2008: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2007: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2006: ¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 2005: ¥2,700,000 (Direct Cost: ¥2,700,000)
Keywords可積分系 / 一般超幾何微分方程式 / 可解格子模型 / Bethe仮説 / 一般化超幾何微分方程式 / 超幾何函数 / 量子群 / Macdonald多項式 / 箱玉系 / ソリトン / 粘性流体
Research Abstract

量子力学系の性質を定量的に記述することは一般には困難であるがその中で完全積分可能系と呼ばれるクラスに関しては多少とも詳しい記述が可能であると思われている. これまでの研究の多くはそのような系をある種の無限次元代数系の表現論と関連づける形でなされてきている. 本研究においてはそのような関連をほかの諸分野, たとえばフックス型微分方程式の理論などと関連づけるなどにより拡げることにより幅広い手法の適用可能性を示した

Report

(5 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (32 results)

All 2009 2008 2007 2006 2005 Other

All Journal Article (22 results) (of which Peer Reviewed: 12 results) Presentation (8 results) Book (2 results)

  • [Journal Article] On differential equations of von Gehlen and Roan2009

    • Author(s)
      Etsuro Date
    • Journal Title

      Glasgow Mathematical Journal vol.51

      Pages: 43-48

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On differential equations of von Gehlen and Roan2009

    • Author(s)
      伊達 悦朗
    • Journal Title

      Glasgow Mathematical Journal 51

      Pages: 43-48

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Behaviour of the Fokker-Planck-Boltzmann equation near a Maxwellian2008

    • Author(s)
      Hai-Liang Li, Akitaka Matsumura
    • Journal Title

      Arch. Ration. Mech. Anal vol.189

      Pages: 1-44

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic expansion of the Bergman kernel-elementary application of the invariant theory, Complex analysis and its Applications2008

    • Author(s)
      Gen Komatsu
    • Journal Title

      Proc. 15^<th> ICFIDCAA Osaka 2007 OKAMI Studies vol.2

      Pages: 43-63

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Drinfeld second realization of quantum affine superalgebras of D^<(1)>(2, 1 ; x) via the Weyl groupoid2008

    • Author(s)
      I. Heckenberger, F. Spill, A. Torrielli, Hiroyuki Yamane
    • Journal Title

      RIMS Kokyuroku Bessatsu B8

      Pages: 171-216

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A generalization of Coxeter groups, root systems, and Matsumoto's theorem2008

    • Author(s)
      I. Heckenberger, Hiroyuki Yamane
    • Journal Title

      Mathematishe Zeitschrift vol.259

      Pages: 255-276

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A. Schilling, Existence of Kirillov-Reshetikhin crystals for nonexceptional types2008

    • Author(s)
      Masato Okado
    • Journal Title

      Representation Theory vol.12

      Pages: 186-207

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic expansion of the Bergman kernel-elementary application of the invariant theory2008

    • Author(s)
      小松 玄
    • Journal Title

      Complex Analysis and its Applications, OCAMI Studies 2

      Pages: 43-63

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A (q, γ) analog of the W_<1+∞> algebra2007

    • Author(s)
      Kei Miki
    • Journal Title

      Journal of Mathematical Physics vol.48

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A (q,γ) analog of the W_1+∞ algebra2007

    • Author(s)
      三木 敬
    • Journal Title

      Journal of Mathematical Physics 48

      Pages: 123520-35

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representations of a Z/3Z-quantum group2007

    • Author(s)
      山根 宏之
    • Journal Title

      Publications of RIMS, Kyoto University 43

      Pages: 75-93

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representations of a Z/3Z-Quantum Group2007

    • Author(s)
      山根 宏之
    • Journal Title

      Publications of RIMS, Kyoto University 43

      Pages: 75-93

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Some quotient algebras arising from the quantum toroidal algebra2006

    • Author(s)
      三木 敬
    • Journal Title

      Osaka Journal of Mathematics 43

      Pages: 895-922

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Existence and stability of steady-state of one-dimensional quantum Euler-Poisson system for semiconductors2006

    • Author(s)
      H.Li, F.Huang, A.Matumura
    • Journal Title

      Journal of differential Equations 225

      Pages: 1-25

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The relaxation-time limit in the quantum hydrodynamic equations for semiconductors2006

    • Author(s)
      A.Jungel, H-L.Li, A.Matsumura
    • Journal Title

      Journal of differential Equations 225

      Pages: 440-464

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Stability of contact discontinuities for the 1-D compressible Navier-Stokes equations2006

    • Author(s)
      F.Huang, A.Matsumura, Z.Xin
    • Journal Title

      Archive for Rational Mechanics and Analysis 179・1

      Pages: 55-77

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Construction of hypergeometric solutions to the q-Painleve equations2005

    • Author(s)
      K. Kajiwara, T. Masuda, Masatoshi Noumi, Y. Ohta, Y. Yamada
    • Journal Title

      International Mathematical Research Notice no.24

      Pages: 1441-1463

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Sharp lower bound for the lifespan of systems of semilinear wave Equations with multiple speeds2005

    • Author(s)
      S.Katayama, A.Matsumura
    • Journal Title

      Jour.Math.Kyoto University 45・2

      Pages: 391-403

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Some quotient algebras arising from the quantum toroidal algebra U_q(sl_2(C_gamma))2005

    • Author(s)
      K.Miki
    • Journal Title

      Osaka Jour.Math. 42

      Pages: 885-929

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Box-ball system with reflecting end2005

    • Author(s)
      A.Kuniba, M.Okado, Y.Yamada
    • Journal Title

      Jour.Nonlinear Math.Phys. 12

      Pages: 475-507

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Construction of hypergeometric solutions to the q-Painleve equations2005

    • Author(s)
      K.Kajiwara, T.Masuda, M.Noumi, Y.Ohta, Y.Yamada
    • Journal Title

      IMRN 24

      Pages: 1141-1463

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Representations of a Z/3Z-Quantum groups

    • Author(s)
      H.Yamane
    • Journal Title

      Publ.RIMS Kyoto Univ. (掲載決定)

    • Related Report
      2005 Annual Research Report
  • [Presentation] 一次元圧縮性粘性流体の長時間挙動2008

    • Author(s)
      松村 昭孝
    • Organizer
      九州非線形偏微分方程式冬の学校
    • Place of Presentation
      九州大学箱崎キャンパス工学部本館
    • Year and Date
      2008-11-22
    • Related Report
      2008 Final Research Report
  • [Presentation] Plain Algorithms2008

    • Author(s)
      Noriaki Kawanaka
    • Organizer
      Combinatorics and Representation Theory
    • Place of Presentation
      名古屋大学多元数理科学研究科
    • Year and Date
      2008-09-03
    • Related Report
      2008 Final Research Report
  • [Presentation] superintegrable chiral Potts模型に現れる多項式と一般超幾何微分方程式2007

    • Author(s)
      伊達 悦朗
    • Organizer
      アクセサリー・パラメータ研究会2007
    • Place of Presentation
      熊本大学 自然科学研究科
    • Year and Date
      2007-10-09
    • Related Report
      2008 Final Research Report
  • [Presentation] Large time behaviors of solutions for the equations of one dimensional motion of viscous and heat conductiove gas2007

    • Author(s)
      松村 昭孝
    • Organizer
      21世紀COE国際会議「機能数理学の構築と展開」
    • Place of Presentation
      福岡市リーセントホテル
    • Year and Date
      2007-10-01
    • Related Report
      2007 Annual Research Report
  • [Presentation] Asymptotic expansion of the Bergman kernel-elementary application of the invariant theory2007

    • Author(s)
      小松 玄
    • Organizer
      The 15th international Conference on Finite or Infinite Dimensional Complex Analysis and Application
    • Place of Presentation
      大阪市立大学 学術総合センター
    • Year and Date
      2007-08-01
    • Related Report
      2007 Annual Research Report
  • [Presentation] On differential equations of von Gehlen and Roan2007

    • Author(s)
      Etsuro Date
    • Organizer
      ISLAND3 Algebraic Aspects of integrable systems
    • Place of Presentation
      Islay, Scotland
    • Year and Date
      2007-07-06
    • Related Report
      2008 Final Research Report
  • [Presentation] On differential equations of von Gehlen-Roan and Roan2007

    • Author(s)
      伊達 悦朗
    • Organizer
      ISLAND3 Algebraic Aspects of integrable systems
    • Place of Presentation
      Islay, Scotland, United Kingdom
    • Year and Date
      2007-07-06
    • Related Report
      2007 Annual Research Report
  • [Presentation] Hadamard's variations in several complex variables, Complex Analysis2005

    • Author(s)
      Gen Komatsu
    • Organizer
      Differential Geometry and Partial Differential Equations(Conference in Honor of the 80^<th> Birthday of Masatake Kuranishi)
    • Place of Presentation
      Columbia大学数学教室
    • Year and Date
      2005-05-03
    • Related Report
      2008 Final Research Report
  • [Book] Encyclopedia of Mathematical Physics(vol.679+729+645+673+549 pages (vol.4, pp594-602 Solitons and Kac-Moody Lie algebra の項を担当))2006

    • Author(s)
      Etsuro Date
    • Publisher
      Elsevier
    • Related Report
      2008 Final Research Report
  • [Book] "Encyclopedia of Mathematical Physics"中の Solitons and Kac-Moody Lie algebra の項2006

    • Author(s)
      伊達 悦朗
    • Total Pages
      9
    • Publisher
      Elsevier
    • Related Report
      2006 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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