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Research on a point of contact between classical and quantum integrable systems

Research Project

Project/Area Number 19540228
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KAKEI Saburo  Rikkyo University, 理学部, 教授 (60318798)

Co-Investigator(Kenkyū-buntansha) KIKUCHI Tetsuya  東京大学, 大学院・数理科学研究科, 研究拠点形成特任研究員 (00374900)
SAITO Yoshihisa  東京大学, 大学院・数理科学研究科, 准教授 (20294522)
NISHIZAWA Michitomo  弘前大学, 教育学部, 准教授 (20318801)
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsソリトン / パンルヴェ方程式 / ヤン・バクスター写像 / shifted Jack多項式 / 可積分系 / 相似簡約 / KP階層 / ガルニエ系 / 行列積分 / KZ方程式 / Jack多項式 / ランダム行列
Research Abstract

Research on integrable systems may be divided into two categories : "classical integrable systems" and "quantum integrable systems". Preceding results suggest the deep relationship between these categories. We devote our attention mainly to two topics : (1) matrix integral solutions to Painleve equations, (2) discrete integrable systems and Yang-Baxter maps. We introduced new formulation for these two topics and obtained several new results. Furthermore, we have carried out research into special functions and obtained several results.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (70 results)

All 2011 2010 2009 2008 2007 Other

All Journal Article (23 results) (of which Peer Reviewed: 13 results) Presentation (41 results) Remarks (6 results)

  • [Journal Article] Max-plus再帰方程式の逆超離散化2011

    • Author(s)
      難波寛,筧三郎
    • Journal Title

      九州大学応用力学研究所 研究集会報告 22AO-S8

      Pages: 248-253

    • Related Report
      2010 Final Research Report
  • [Journal Article] Indecomposable decomposition of tensor products of modules over the restricted quantum universal enveloping algebra associated to sl22011

    • Author(s)
      H.Kondo, Y.Saito
    • Journal Title

      J.Alg. 330

      Pages: 103-129

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Max-plus再帰方程式の逆超離散化2011

    • Author(s)
      難波寛, 筧三郎
    • Journal Title

      九州大学応用力学研究所 研究集会報告

      Volume: 22AO-S8 Pages: 248-253

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Yang-Baxter maps from the discrete BKP equation2010

    • Author(s)
      S.Kakei, J.J.C. Nimmo, R.Willox
    • Journal Title

      SIGMA (Integrability and Geometry : Methods and Applications) 6

      Pages: 28-28

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 離散BKP方程式とYang-Baxter写像2010

    • Author(s)
      筧三郎, J.J.C.Nimmo, R.Willox
    • Journal Title

      九州大学応用力学研究所研究集会報告 21ME-S7

      Pages: 214-219

    • Related Report
      2010 Final Research Report
  • [Journal Article] Representation Theory of Algebraic Groups and Quantum Groups2010

    • Author(s)
      Y.Saito, M.Shiota
    • Journal Title

      Double affine Hecke algebras and elliptic Hecke algebras, Progress in Math. 284

      Pages: 297-312

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Yang-Baxter Maps from the Discrete BKP Equation2010

    • Author(s)
      S. Kakei, J. J. C. Nimmo, R. Willox
    • Journal Title

      SIGMA 6

      Pages: 28-28

    • Related Report
      2009 Self-evaluation Report
  • [Journal Article] Yang-Baxter Maps from the Discrete BKP Equation2010

    • Author(s)
      筧三郎, J.J.C.Nimmo, R.Willox
    • Journal Title

      Symmetry, Integrability and Geometry : Methods and Applications(SIGMA) 6

      Pages: 28-28

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 離散BKP方程式と Yang-Baxter 写像2010

    • Author(s)
      筧三郎, J.J.C.Nimmo, R.Willox
    • Journal Title

      九州大学応用力学研究所研究集会報告集 21ME-S7

      Pages: 142-148

    • Related Report
      2009 Annual Research Report
  • [Journal Article] The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials2009

    • Author(s)
      S.Kakei, M.Nishizawa, Y.Saito, Y.Takeyama
    • Journal Title

      SIGMA (Symmetry, Integrability and Geometry : Methods and Applications) 5

      Pages: 10-10

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Yang-Baxter Maps and the Discrete KP Hierarchy2009

    • Author(s)
      S.Kakei, J.J.C.Nimmo, R.Willox
    • Journal Title

      Glasgow Mathematical Journal 51巻OA号

      Pages: 107-119

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] AKNS-ASDYM階層とパンルヴェ方程式2009

    • Author(s)
      筧三郎,菊地哲也
    • Journal Title

      京都大学数理解析研究所講究録 1662

      Pages: 195-210

    • Related Report
      2010 Final Research Report
  • [Journal Article] Yang-Baxter maps from the discrete KP hierarchy2009

    • Author(s)
      筧三郎, R.Willox, J.J.C.Nimmo
    • Journal Title

      京都大学数理解析研究所講究録 1650

      Pages: 162-172

    • Related Report
      2010 Final Research Report
  • [Journal Article] On Hecke algebras associated with elliptic root systems andthe double affine Hecke algebras2009

    • Author(s)
      Y.Saito, M.Shiota
    • Journal Title

      Publ.RIMS, Kyoto Univ. 45

      Pages: 845-905

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Yang-Baxter Maps and the Discrete KP Hierarchy2009

    • Author(s)
      S. Kakei, J. J. C. Nimmo, R. Willox
    • Journal Title

      Glasgow Mathematical Journal 51巻0A号

      Pages: 107-119

    • Related Report
      2009 Self-evaluation Report
  • [Journal Article] The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials2009

    • Author(s)
      S. Kakei, M. Nishizawa, Y. Saito, Y. Takeyama
    • Journal Title

      SIGMA 5

      Pages: 10-10

    • Related Report
      2009 Self-evaluation Report
  • [Journal Article] AKNS-ASDYM階層とパンルヴェ方程式2009

    • Author(s)
      筧三郎, 菊地哲也
    • Journal Title

      京都大学数理解析研究所講究録 1662

      Pages: 195-210

    • Related Report
      2009 Annual Research Report
  • [Journal Article] Yang-Baxter Maps and the Discrete KP Hierarchy2009

    • Author(s)
      S. Kakei, J. J. C. Nimmo, R. Willox
    • Journal Title

      Glasgow Mathematical Journal 51巻OA号

      Pages: 107-119

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Rational qKZ Equation and Shifted Non-Symmetric Jack Polynomials2009

    • Author(s)
      S. Kakei, M. Nishizawa, Y. Saito, Y. Takeyama
    • Journal Title

      Symmetry, Integrability and Geometry : Methods and Applications (SIGMA) 5

      Pages: 10-10

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 超幾何関数で表される不変量を持つ差分方程式2007

    • Author(s)
      榊武史,筧三郎
    • Journal Title

      日本応用数理学会論文誌 17巻4号

      Pages: 455-462

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 離散確率過程とq-超幾何関数2007

    • Author(s)
      何健志,筧三郎,北根靖史
    • Journal Title

      日本応用数理学会論文誌 17巻4号

      Pages: 463-468

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] 超幾何関数で表される不変量を持つ差分方程式2007

    • Author(s)
      榊 武史, 筧 三郎
    • Journal Title

      日本応用数理学会論文誌 17巻4号

      Pages: 455-462

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 離散確率過程とq-超幾何関数2007

    • Author(s)
      何 健志, 筧 三郎, 北根 靖史
    • Journal Title

      日本応用数理学会論文誌 17巻4号

      Pages: 463-468

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] From discrete KP to Yang-Baxter maps, GCOE conference2010

    • Author(s)
      筧三郎
    • Organizer
      Algebraic and geometric aspects of discrete integrable systems
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2010-12-14
    • Related Report
      2010 Final Research Report
  • [Presentation] From discrete KP to Yang-Baxter maps2010

    • Author(s)
      筧三郎
    • Organizer
      GCOE conference : Algebraic and geometric aspects of discrete integrable systems
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2010-12-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] Max-plus再帰方程式の逆超離散化2010

    • Author(s)
      難波寛,筧三郎
    • Organizer
      非線形波動研究の新たな展開-現象とモデル化-
    • Place of Presentation
      九州大学応用力学研究所
    • Year and Date
      2010-10-29
    • Related Report
      2010 Final Research Report
  • [Presentation] Max-plus再帰方程式の逆超離散化2010

    • Author(s)
      難波寛, 筧三郎
    • Organizer
      非線形波動研究の新たな展開 -現象とモデル化-
    • Place of Presentation
      九州大学応用力学研究所
    • Year and Date
      2010-10-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] Construction of Yang-Baxter maps from discrete KP2010

    • Author(s)
      筧三郎
    • Organizer
      Satellite conference of the ICM 2010, Integrable Systems and Geometry
    • Place of Presentation
      Pondicherry大学(インド)
    • Year and Date
      2010-08-16
    • Related Report
      2010 Final Research Report
  • [Presentation] Construction of Yang-Baxter maps from discrete KP2010

    • Author(s)
      筧三郎
    • Organizer
      Satellite conference of the ICM 2010, "Integrable Systems and Geometry"
    • Place of Presentation
      Pondicherry大学(インド)
    • Year and Date
      2010-08-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] 離散BKP方程式とYang-Baxter写像2010

    • Author(s)
      筧三郎, J.J.C.Nimmo, R.Willox
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶応義塾大学
    • Year and Date
      2010-03-26
    • Related Report
      2010 Final Research Report
  • [Presentation] 離散BKP方程式と Yang-Baxter 写像2010

    • Author(s)
      筧三郎
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶應義塾大学矢上キャンパス
    • Year and Date
      2010-03-26
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] 離散BKP方程式とYang-Baxter 写像2010

    • Author(s)
      筧三郎, J.J.C.Nimmo, R.Willox
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶應義塾大学矢上キャンパス
    • Year and Date
      2010-03-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] 離散可積分系入門2010

    • Author(s)
      筧三郎
    • Organizer
      九州大学産業技術数理研究センターワークショップ"離散可積分系・離散微分幾何チュートリアル"
    • Place of Presentation
      九州大学
    • Year and Date
      2010-02-22
    • Related Report
      2010 Final Research Report
  • [Presentation] Bernstein-Zelevinsky data and the crystal basis of U_q^-$ in type A_<n-1>(1)2010

    • Author(s)
      斉藤義久
    • Organizer
      組合せ論的表現論とその応用
    • Place of Presentation
      京都大学
    • Related Report
      2010 Final Research Report
  • [Presentation] Mirkovic-Vilonen polytopes and quiver construction of crystal basis in type A2010

    • Author(s)
      斉藤義久
    • Organizer
      Representation Theory of Algebraic Groups and Quantum Groups'10
    • Place of Presentation
      名古屋大学
    • Related Report
      2010 Final Research Report
  • [Presentation] Crystals, MV-polytopes and 'tropical flag varieties'2010

    • Author(s)
      斉藤義久
    • Organizer
      トロピカル幾何と超離散系の新展開
    • Place of Presentation
      京都大学大学院工学研究科
    • Related Report
      2010 Final Research Report
  • [Presentation] 離散BKP方程式とYang-Baxter写像2009

    • Author(s)
      筧三郎, J.J.C.Nimmo, R.Willox
    • Organizer
      研究集会:非線形波動研究の現状と将来-次の10年への展望
    • Place of Presentation
      九州大学応用力学研究所
    • Year and Date
      2009-11-21
    • Related Report
      2010 Final Research Report
  • [Presentation] 離散BKP方程式と Yimg-Baxter写像2009

    • Author(s)
      筧三郎, J.J.C.Nimmo, R.Willox
    • Organizer
      研究集会「非線形波動研究の現状と将来」
    • Place of Presentation
      九州大学応用力学研究所
    • Year and Date
      2009-11-21
    • Related Report
      2009 Annual Research Report
  • [Presentation] Yang-Baxter maps arising from the BKP hierarchy2009

    • Author(s)
      筧三郎, J.J.C.Nimmo, R.Willox
    • Organizer
      Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems
    • Place of Presentation
      グラスゴー大学(英国)
    • Year and Date
      2009-04-01
    • Related Report
      2009 Annual Research Report
  • [Presentation] AKNS-ASDYM階層とパンルヴェ方程式2009

    • Author(s)
      筧 三郎, 菊地哲也
    • Organizer
      京都大学数理解析研究所短期共同「微分方程式のモノドロミーをめぐる諸問題」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-02-06
    • Related Report
      2008 Annual Research Report
  • [Presentation] The rational qKZ equation and shifted non-symmetric Jack polynomials2009

    • Author(s)
      筧三郎,西澤道知,斉藤義久,竹山美宏
    • Organizer
      日本数学会2009年度年会
    • Place of Presentation
      東京大学
    • Related Report
      2010 Final Research Report
  • [Presentation] ソリトン方程式の保存則と相似簡約2008

    • Author(s)
      菊地 哲也
    • Organizer
      2007函数方程式論サマーセミナー
    • Place of Presentation
      ビレッジ安曇野(長野県安曇野市)
    • Year and Date
      2008-08-07
    • Related Report
      2007 Annual Research Report
  • [Presentation] 離散KP階層とYang-Baxter map2008

    • Author(s)
      筧三郎, J.J.C.Nimmo, R.Willox
    • Organizer
      日本数学会2008年度年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-23
    • Related Report
      2010 Final Research Report
  • [Presentation] NLS-AKNS階層とパンルヴェ方程式2008

    • Author(s)
      筧三郎,菊地哲也
    • Organizer
      日本数学会2008年度年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-23
    • Related Report
      2010 Final Research Report
  • [Presentation] 離散KP階層とYang-Baxter map2008

    • Author(s)
      筧 三郎
    • Organizer
      日本数学会2008年度年会
    • Place of Presentation
      近畿大学理工
    • Year and Date
      2008-03-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] NLS-ASDYM階層とパンルヴェ方程式2008

    • Author(s)
      菊地 哲也
    • Organizer
      日本数学会2008年度年会
    • Place of Presentation
      近畿大学理工
    • Year and Date
      2008-03-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] 2+1次元NLS階層とパンルヴェ方程式2008

    • Author(s)
      菊地 哲也
    • Organizer
      古典解析セミナー
    • Place of Presentation
      大阪大学理学部
    • Year and Date
      2008-02-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] 2+1次元NLS階層の相似簡約2008

    • Author(s)
      菊地 哲也
    • Organizer
      可積分系ウィンターセミナー2008
    • Place of Presentation
      KKR湯沢ゆきぐに(新潟県南魚沼郡)
    • Year and Date
      2008-02-19
    • Related Report
      2007 Annual Research Report
  • [Presentation] 2+1次元NLS階層とパンルヴェ方程式2008

    • Author(s)
      菊地 哲也
    • Organizer
      神戸可積分系セミナー
    • Place of Presentation
      神戸大学自然科学研究科
    • Year and Date
      2008-01-16
    • Related Report
      2007 Annual Research Report
  • [Presentation] Hecke代数の多項式表現について2008

    • Author(s)
      斉藤義久
    • Organizer
      第53回代数学シンポジウム
    • Place of Presentation
      盛岡駅前アイーナ
    • Related Report
      2010 Final Research Report
  • [Presentation] 矢嶋・及川方程式とパンルヴェV2007

    • Author(s)
      筧 三郎
    • Organizer
      研究集会「ソリトンの数理とその応用:非線形波動から可積分系へ」
    • Place of Presentation
      湯田簡易保険保養センター(山口県山口市)
    • Year and Date
      2007-12-22
    • Related Report
      2007 Annual Research Report
  • [Presentation] 戸田階層とパンルヴェ方程式2007

    • Author(s)
      菊地哲也
    • Organizer
      2007年度表現論シンポジウム
    • Place of Presentation
      休暇村讃岐五色台
    • Year and Date
      2007-11-14
    • Related Report
      2010 Final Research Report
  • [Presentation] 戸田階層とパンルヴェ方程式2007

    • Author(s)
      菊地 哲也
    • Organizer
      2007年度表現論シンポジウム
    • Place of Presentation
      休暇村讃岐五色台(香川県坂出市)
    • Year and Date
      2007-11-14
    • Related Report
      2007 Annual Research Report
  • [Presentation] Similarity solutions of NLS-SDYM hierarchy and matrix integrals2007

    • Author(s)
      筧三郎
    • Organizer
      DMHF2007 : COE Conference on the Development of Dynamic Mathematics with High Functionality
    • Place of Presentation
      福岡リーセントホテル
    • Year and Date
      2007-10-02
    • Related Report
      2010 Final Research Report
  • [Presentation] Similarity Solutions of NLS-SDYM Hierarchy and Matrix Integrals, DMHF20072007

    • Author(s)
      筧三郎
    • Organizer
      COE Conference on the Development of Dynamic Mathematics with High Functionality
    • Place of Presentation
      福岡リーセントホテル
    • Year and Date
      2007-10-02
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Similarity solutions of NLS-SDYM hierarchy and matrix integrals2007

    • Author(s)
      筧 三郎
    • Organizer
      DMHF2007:COE Conference on the Development of Dynamic Mathematics with High Functionality
    • Place of Presentation
      福岡リーセントホテル
    • Year and Date
      2007-10-02
    • Related Report
      2007 Annual Research Report
  • [Presentation] 二重アフィンヘッケ代数と楕円ヘッケ代数について2007

    • Author(s)
      斉藤 義久
    • Organizer
      代数セミナー
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2007-09-27
    • Related Report
      2007 Annual Research Report
  • [Presentation] Yang-Baxter maps from the discrete KP hierarchy2007

    • Author(s)
      筧三郎, J.J.C.Nimmo, R.Willox
    • Organizer
      研究集会:可積分数理の新潮流
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-08-22
    • Related Report
      2010 Final Research Report
  • [Presentation] Yang-Baxter Maps from the Discrete KP Hierarchy2007

    • Author(s)
      筧三郎
    • Organizer
      研究集会「可積分数理の新潮流」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-08-22
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] Yang-Baxter maps from the discrete KP hierarchy2007

    • Author(s)
      筧 三郎
    • Organizer
      研究集会「可積分数理の新潮流」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-08-22
    • Related Report
      2007 Annual Research Report
  • [Presentation] ソリトン方程式の保存則と相似簡約2007

    • Author(s)
      菊地哲也
    • Organizer
      2007函数方程式論サマーセミナー
    • Place of Presentation
      ビレッジ安曇野
    • Year and Date
      2007-08-07
    • Related Report
      2010 Final Research Report
  • [Presentation] 有限次元代数の表現論入門2007

    • Author(s)
      斉藤 義久
    • Organizer
      代数幾何セミナー2007
    • Place of Presentation
      東京大学玉原国際セミナーハウス(群馬県沼田市)
    • Year and Date
      2007-08-06
    • Related Report
      2007 Annual Research Report
  • [Presentation] Local Darboux transformations and geometric crystals, International workshop2007

    • Author(s)
      筧三郎, J.J.C.Nimmo, R.Willox
    • Organizer
      ISLAND 3(Integrable Systems : Linear And Nonlinear Dynamics)
    • Place of Presentation
      Islay, Scotland
    • Year and Date
      2007-07-04
    • Related Report
      2010 Final Research Report
  • [Presentation] Local Darboux transformations and geometric crystals2007

    • Author(s)
      筧 三郎
    • Organizer
      International workshop"ISLAND3"(Integrable Systems:Linear And Nonlinear Dynamics)
    • Place of Presentation
      Islay,UK
    • Year and Date
      2007-07-04
    • Related Report
      2007 Annual Research Report
  • [Remarks] ホームページ等

    • URL

      http://www.rkmath.rikkyo.ac.jp/~kakei/

    • Related Report
      2010 Final Research Report
  • [Remarks]

    • URL

      http://www.rkmath.rikkyo.ac.jp/~kakei/

    • Related Report
      2010 Annual Research Report
  • [Remarks] 研究代表者ホームページ

    • URL

      http://www.rkmath.rikkyo.ac.jp/~kakei/

    • Related Report
      2009 Self-evaluation Report
  • [Remarks]

    • URL

      http://www.rkmath.rikkyo.ac.jp/~kakei/

    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://www.rkmath.rikkyo.ac.jp/~kakei/

    • Related Report
      2008 Annual Research Report
  • [Remarks]

    • URL

      http://www.rkmath.rikkyo.ac.jp/~kakei/

    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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