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2013 Fiscal Year Final Research Report

Quantum discrete isomonodromy system from the viewpoint of quantum Teichmueller space

Research Project

  • PDF
Project/Area Number 23540004
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionTohoku University

Principal Investigator

HASEGAWA Koji  東北大学, 理学(系)研究科(研究院), 准教授 (30208483)

Co-Investigator(Renkei-kenkyūsha) KUROKI Gen  東北大学, 大学院・理学研究科, 助教 (10234593)
Project Period (FY) 2011 – 2013
Keywords量子群
Research Abstract

The aim is to construct the quantum discretized version of the monodromy preserbing deformation of the Fuchsian equation as the system on the discretized Teichmueller space, so that one can recognize the Painleve VI system as well as the Garnier system as included into the picture, aiming that the construction will give the understanding of the symmetry structure as well as the viewpoint to the solvable lattice models from the theory of Riemann surfaces.
For this aim we have succeeded in the rank two case the construction of the quantum discrete version of the isomonodromy system using the periodically reduced system of the nonautonomous discrete quantum Toda field equation. The autonomous system has been studied by Kashaev and Reshetikhin, and our result is in good coincidence with our previous result using the Weyl group action approach.

  • Research Products

    (8 results)

All 2014 2013 2012 2011

All Journal Article (2 results) (of which Peer Reviewed: 2 results) Presentation (6 results)

  • [Journal Article] Quantizing the Painleve VI equation : The Lax formalism2013

    • Author(s)
      Koji Hasegawa
    • Journal Title

      Lett. Math. Phys

      Volume: 103 no.8 Pages: 865-879

    • Peer Reviewed
  • [Journal Article] Quantizing the Bäcklund transforma -tions of Painlevé equations and the quantum discrete Painlevé VI equa -tion2011

    • Author(s)
      Koji Hasegawa
    • Journal Title

      Advanced Studies in Pure Mathematics 61"Exploration of New Structures and Natural Constructions in Mathematical Physics", Japan Math. Soc

      Pages: 275-288

    • Peer Reviewed
  • [Presentation] パンルヴェ系τ 函数の量子化について2014

    • Author(s)
      黒木玄
    • Organizer
      東京可積分系セミナー
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2014-02-15
  • [Presentation] 量子離散ガルニエ系のラックス形式2013

    • Author(s)
      Koji Hasegawa
    • Organizer
      日本数学会秋季総合分科会, 無限可積分系セッション一般講演
    • Place of Presentation
      愛媛大学
    • Year and Date
      2013-09-24
  • [Presentation] Weyl 群双有理作用とτ函数の量子化-量子化されたτ函数の正則性2013

    • Author(s)
      黒木玄
    • Organizer
      日本数学会「無限可積分系セッション」一般講演
    • Place of Presentation
      東京理科大学神楽坂キャンパス
    • Year and Date
      2013-03-28
  • [Presentation] 互いに素なm, n に対する拡大アフィンWeyl 群の直積$¥widetilde{W}(A^{(1)}_{m-1})¥times¥ widetilde{W}(A^{(1)}_{n-1})$の双有理作用の量子化2013

    • Author(s)
      黒木玄
    • Organizer
      日本数学会
    • Place of Presentation
      京都大学
    • Year and Date
      2013-03-22
  • [Presentation] 量子離散パンルヴェVI 型方程式のラックス形式2012

    • Author(s)
      Koji Hasegawa
    • Organizer
      日本数学会秋季総合分科会, 無限可積分系セッション一般講演
    • Place of Presentation
      九州大学
    • Year and Date
      2012-09-18
  • [Presentation] 量子Weyl 群双有理作用のSato-Wilson 表示2012

    • Author(s)
      黒木玄
    • Organizer
      日本数学会「無限可積分系セッション」一般講演
    • Place of Presentation
      九州大学伊都キャンパス
    • Year and Date
      2012-09-18

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Published: 2015-07-16  

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