• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Free field approach to solvable models associated with elliptic algebra

Research Project

Project/Area Number 26400105
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionYamagata University

Principal Investigator

Kojima Takeo  山形大学, 大学院理工学研究科, 教授 (80307800)

Project Period (FY) 2014-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords量子可積分系 / 量子群 / 自由場表示 / 超代数 / 頂点作用素 / 可解模型 / 開境界条件 / スクリーニング / 可積分系 / 量子W代数 / スクリーニング作用素 / アフィン・リー環 / 自由場表現 / 交換関係 / アフィン・リー代数 / Wakimoto表現 / スピン鎖 / Boundary Yang-Baxter 方程式 / 脇本表現 / 熱力学的極限 / 超対称性 / テータ関数 / 国際研究者交流(フランス)
Outline of Final Research Achievements

We study quantum integrable systems by the vertex operator approach. We focus our attention on free field approach (bosonization) of symmetry, vertex operator, and ground state. The most outstanding result is (A) a bosonization of quantum superalgebra Uq(sl(M|N)^) for an arbitrary level k. We also obtaion (B) integral representations of correlation functions and form factors of the XXZ chain with a triangular boundary, (C) a bosonization of ground state of quantum superalgebra Uq(gl(N|N)^)-analogue of XXZ chain with a diagonal boundary, and (D) a direct proof of commutation relations of vertex operators for quantum superalgebra Uq(sl(M|N)^) for level k=1.

Academic Significance and Societal Importance of the Research Achievements

頂点作用素の方法による量子可積分系の研究に、新たな可能性を広げた。特に、真に新しい例の構成を通じて、頂点作用素の方法の適用範囲を広げた。まず、対角でない開境界での相関関数の積分表示の構成の最初の例を与えた。さらに、量子群の一般のレベルkでの自由場表示の構成は、わずか2つの例( Uq(sl(N)^) および Uq(sl(M|N)^))しか知られていないが、そのうちの1つが本研究において構成された。また、Uq(sl(M|N))^) の頂点作用素の交換子関係の直接証明により、楕円超代数 Uqp(sl(M|N)^) の頂点作用素の構成に向けた道筋がつけられた。

Report

(6 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (21 results)

All 2018 2017 2016 2015 2014 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results,  Acknowledgement Compliant: 4 results) Presentation (10 results) (of which Int'l Joint Research: 6 results,  Invited: 7 results) Remarks (4 results)

  • [Journal Article] Wakimoto realization of the quantum affine superalgebra Uq(sl^(M|N))2018

    • Author(s)
      Takeo Kojima
    • Journal Title

      Springer Proceedings

      Volume: 263 Pages: 149-163

    • DOI

      10.1007/978-981-13-2715-5_8

    • ISBN
      9789811327148, 9789811327155
    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Commutation relations of vertex operators for Uq(sl(M|N)^)2018

    • Author(s)
      Takeo Kojima
    • Journal Title

      Journal of Mathematical Physics

      Volume: 355 Issue: 10 Pages: 603-644

    • DOI

      10.1063/1.5047255

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wakimoto realization of the quantum affine superalgebra $U_q(\hat{sl}(M|N))$2018

    • Author(s)
      Takeo Kojima
    • Journal Title

      Springer Proceedings

      Volume: 印刷中

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] A bosonization of Uq(sl(M|N)^)2017

    • Author(s)
      Takeo Kojima
    • Journal Title

      Communication in Mathematical Physics

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Boundary state of a Uq(gl^(N|N)) analogue of half-infinite t-J model2016

    • Author(s)
      Takeo Kojima
    • Journal Title

      Journal of Statitical Maechanics

      Volume: 014 Issue: 2 Pages: 023108-023108

    • DOI

      10.1088/1742-5468/2016/02/023108

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Vertex operator approach to semi-infinite spin chain : recent progress,2014

    • Author(s)
      Takeo Kojima
    • Journal Title

      Springer Proceedings in Mathematics and Statistics

      Volume: 111 Pages: 265-277

    • DOI

      10.1007/978-4-431-55285-7_18

    • ISBN
      9784431552840, 9784431552857
    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Form factors of the half-infinite XXZ spin chain with a triangular boundary2014

    • Author(s)
      Pascal Baseilhac and Takeo Kojima
    • Journal Title

      Journal of Statistical Mechanics

      Volume: P09004 Issue: 9 Pages: P09004-P09004

    • DOI

      10.1088/1742-5468/2014/09/p09004

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] A bosonization of Uq(sl(M|N)^)2018

    • Author(s)
      Takeo Kojima
    • Organizer
      The 32nd International Colloquium on Group Theoretical Methods in Physics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Wakimoto realization of the quantum superalgebra U_q(sl(M|N)^)2017

    • Author(s)
      Takeo Kojima
    • Organizer
      Lie Theoey and Its Application in Physics 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A bosonization of U_q(sl((M|N)^)2017

    • Author(s)
      Takeo Kojima
    • Organizer
      Mathematical Physics Meeting 2017
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A Bosonization of $Uq(\hat{sl}(M|N))$2017

    • Author(s)
      小島武夫
    • Organizer
      日本数学会
    • Related Report
      2017 Research-status Report
  • [Presentation] A bosonization of Uq(sl(M|N)^)2017

    • Author(s)
      Takeo Kojima
    • Organizer
      Seminar at University of Leeds
    • Place of Presentation
      University of Leeds(England)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A bosonization of Uq(sl(M|N)^)2017

    • Author(s)
      Takeo Kojima
    • Organizer
      Seminar at University of Lyon
    • Place of Presentation
      University of Lyon(France)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Level k bosonization of Uq(sl(M|N)^)2016

    • Author(s)
      Takeo Kojima
    • Organizer
      Seminar at University of Tours
    • Place of Presentation
      University of Tours (France)
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Boundary state of a Uq(gl^(N|N)) analogue of half-infinite t-J model2015

    • Author(s)
      Takeo Kojima
    • Organizer
      Seminar at University of Tours
    • Place of Presentation
      University of Tours (France)
    • Year and Date
      2015-09-15
    • Related Report
      2015 Research-status Report
  • [Presentation] Vertex operator approach to semi-infinite spin chain : recent progress2014

    • Author(s)
      Takeo Kojima
    • Organizer
      Worhshop: Search for Classical Analysis and Quantum Integrable Systems
    • Place of Presentation
      Kyoto University, Kyoto, Japan
    • Year and Date
      2014-11-17
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Vertex operator approach to semi-infinite spin chain : recent progres2014

    • Author(s)
      Takeo Kojima
    • Organizer
      8-th Mathematical Physics Meeting
    • Place of Presentation
      Belgrade, Serbia
    • Year and Date
      2014-08-29
    • Related Report
      2014 Research-status Report
    • Invited
  • [Remarks] Dr.Kojima's homepage

    • URL

      http://bt.yz.yamagata-u.ac.jp/mathematics/kojima/kojima.html

    • Related Report
      2018 Annual Research Report 2016 Research-status Report
  • [Remarks] Dr.Kojima’s Homepage

    • URL

      http://bt.yz.yamagata-u.ac.jp/mathematics/kojima/kojima.html

    • Related Report
      2017 Research-status Report
  • [Remarks] Dr. Kojima's home page

    • URL

      http://kojima.yz.yamagata-u.ac.jp/kojima.html

    • Related Report
      2015 Research-status Report
  • [Remarks] 山形大学工学部・数物学分野 ホームページ

    • URL

      http://kojima.yz.yamagata-u.ac.jp/kojima.html

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2023-03-16  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi