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Representation of elliptic quantum groups and elliptic Ruijsenaars model

Research Project

Project/Area Number 26400046
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionTokyo University of Marine Science and Technology

Principal Investigator

Konno Hitoshi  東京海洋大学, 学術研究院, 教授 (00291477)

Co-Investigator(Renkei-kenkyūsha) JIMBO MICHIO  立教大学, 理学部, 教授 (80109082)
NOUMI MASATOSHI  神戸大学, 大学院理学研究科, 教授 (80164672)
MIMACHI KATSUHISA  大阪大学, 大学院情報科学研究科, 教授 (40211594)
OSHIMA KAZUYUKI  愛知工業大学, 基礎教育センター, 准教授 (30547980)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords楕円量子群 / 楕円Ruijsenaars模型 / 楕円q-KZ方程式 / 量子行列式 / 変形W代数 / Macdonald対称関数 / 楕円超幾何関数 / Rujisenaars模型 / q-KZ方程式 / ヘッケ環 / Macdonald多項式 / アフィン リー環 / 超幾何関数 / 量子群 / ホップ代数 / 楕円関数 / KZ方程式 / 特殊関数 / 楕円量子KZ方程式 / W代数 / アフィンリー環 / Hecke環 / Ruijsenaars模型
Outline of Final Research Achievements

We have formulated the quantum determinant as well as the quantum minor determinants of the L-operators for the face type elliptic quantum group U_q,p(gl_N). We have also obtained a formula for the elliptic half currents in terms of the quantum minor determinants. We then have completed a proof of the isomorphism between U_q,p(gl_N) and the central extension E_q,p(gl_N) of Felder’s elliptic quantum group. In addition, we have obtained formal elliptic hypergeometric integral solutions to the face type elliptic q-KZ equation and associated elliptic weight functions by considering the traces of the product of the intertwining operators of the level-1 U_q,p(sl_N)-modules.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (10 results)

All 2017 2016 2015 2014

All Journal Article (4 results) (of which Peer Reviewed: 4 results,  Acknowledgement Compliant: 4 results) Presentation (6 results) (of which Int'l Joint Research: 3 results,  Invited: 3 results)

  • [Journal Article] Elliptic Quantum Group U_{q,p}(B^{(1)}_N) and Vertex Operators2017

    • Author(s)
      H.Konno and K.Oshima
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B62 Pages: 97-148

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Elliptic Quantum Groups U_{q,p}(gl_N^) and E_{q,p}(sl_N^)2017

    • Author(s)
      H.Konno
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Elliptic Quantum Group U_{q,p}(B_N^(1)) and Vertex Operators2016

    • Author(s)
      H.Konno and K.Oshima
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B Pages: 1-62

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Elliptic Algebra U_qp(g^) and Quantum Z-Algebras2015

    • Author(s)
      R.M.Farghly, H.Konno and K.Oshima
    • Journal Title

      Algebra and Representation Theory

      Volume: 18 Issue: 1 Pages: 103-135

    • DOI

      10.1007/s10468-014-9483-x

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Elliptic Weight Functions and Finite Dimensional Representations of Elliptic Quantum Groups2017

    • Author(s)
      H.Konno
    • Organizer
      Elliptic Hypergeometric Functions in Combinatorics, Integrable Systems and Physics
    • Place of Presentation
      University of Wien, Wien, Austria
    • Year and Date
      2017-03-20
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Elliptic q-KZ Equation and the Weight Functions2016

    • Author(s)
      H.Konno
    • Organizer
      Recent Advances in Quantum Integrable Systems
    • Place of Presentation
      University of Geneva, Geneva, Suitzerland
    • Year and Date
      2016-08-22
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Elliptic q-KZ Equation and the Weight Functions2016

    • Author(s)
      H.Konno
    • Organizer
      Classical and Quantum Integrable Systems
    • Place of Presentation
      Euler International Mathematical Institute, St. Petersburg,Russia
    • Year and Date
      2016-07-11
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 楕円量子群入門2014

    • Author(s)
      今野 均
    • Organizer
      神戸大学集中講義
    • Place of Presentation
      神戸大学理学部数学教室
    • Year and Date
      2014-12-01 – 2014-12-05
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Elliptic Quantum Group, Drinfeld Coproduct and Deformed W-Algebras2014

    • Author(s)
      H.Konno
    • Organizer
      Recent Advances in Quantum Integrable Systems
    • Place of Presentation
      Univ. of Burgundy, Dijon, France
    • Year and Date
      2014-09-01 – 2014-09-05
    • Related Report
      2014 Research-status Report
  • [Presentation] Elliptic Quantum Group U_qp(g^), Drinfeld Coproduct and Deformed W-Algebras2014

    • Author(s)
      H. Konno
    • Organizer
      RIMS Seminar on Representation Theory
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-07-11
    • Related Report
      2014 Research-status Report
    • Invited

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Published: 2014-04-04   Modified: 2018-03-22  

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