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Algebraic analysis of difference equations arising from integrable systems

Research Project

Project/Area Number 26400106
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionUniversity of Tsukuba

Principal Investigator

TAKEYAMA Yoshihiro  筑波大学, 数理物質系, 准教授 (60375392)

Co-Investigator(Renkei-kenkyūsha) NAGOYA Hajime  金沢大学, 数物科学系, 准教授 (80447367)
TANAKA Tatsushi  京都産業大学, 理学部, 准教授 (60515196)
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords可積分系 / 確率過程 / 多重ゼータ値 / q類似 / q 類似 / 可積分確率過程 / アフィンヘッケ代数 / 量子アフィン代数 / 表現論
Outline of Final Research Achievements

We studied algebraic structure of integrable stochastic systems and a q-analogue of multiple zeta values (qMZV). First, we constructed new integrable stochastic systems using a representation of a deformation of the affine Hecke algebra. Regarding the multi-spices q-Boson model, which is an integrable stochastic system constructed as above, we obtained an explicit formula for eigenfunctions of its generator. Second, we found that the finite sum obtained by setting the parameter q in qMZVs to a root of unity simultaneously produces important objects in number theory called finite/symmetrized multiple zeta values.

Report

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

    (13 results)

All 2018 2017 2016 2015 2014

All Journal Article (2 results) (of which Peer Reviewed: 2 results,  Acknowledgement Compliant: 2 results) Presentation (11 results) (of which Int'l Joint Research: 2 results,  Invited: 8 results)

  • [Journal Article] A Discrete Analogue of Periodic Delta Bose Gas and Affine Hecke Algebra2014

    • Author(s)
      Yoshihiro Takeyama
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: 57

    • NAID

      130003391676

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A deformation of affine Hecke algebra and integrable stochastic particle system2014

    • Author(s)
      Yoshihiro Takeyama
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 47 Issue: 46 Pages: 465203-465203

    • DOI

      10.1088/1751-8113/47/46/465203

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] |q|=1における量子KZ方程式と多重正弦関数2018

    • Author(s)
      竹山美宏
    • Organizer
      多重三角関数とその一般化
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] On the eigenfunctions for the multi-species q-Boson system2017

    • Author(s)
      竹山美宏
    • Organizer
      日本数学会年会
    • Place of Presentation
      首都大学東京 南大沢キャンパス (東京都八王子市)
    • Year and Date
      2017-03-26
    • Related Report
      2016 Research-status Report
  • [Presentation] 1のベキ根をパラメータにもつ有限多重調和級数と有限(実)多重ゼータ値2017

    • Author(s)
      竹山美宏
    • Organizer
      関西多重ゼータ研究会
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] 可積分確率過程に現れる対称関数2016

    • Author(s)
      竹山美宏
    • Organizer
      九州大学応用力学研究所 共同利用研究集会「非線形波動研究の深化と展開」
    • Place of Presentation
      九州大学 筑紫キャンパス (福岡県春日市)
    • Year and Date
      2016-11-04
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 可積分確率過程の表現論的構成2016

    • Author(s)
      竹山美宏
    • Organizer
      Algebraic Lie Theory and Representation Theory
    • Place of Presentation
      菅平高原 プチ・ホテル ゾンタック (長野県上田市)
    • Year and Date
      2016-06-11
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Algebraic construction of multi-species q-Boson system2016

    • Author(s)
      Yoshihiro Takeyama
    • Organizer
      Infinite Analysis 16
    • Place of Presentation
      大阪市立大学 (大阪府大阪市)
    • Year and Date
      2016-03-25
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Algebraic construction of multi-species q-Boson system2016

    • Author(s)
      竹山 美宏
    • Organizer
      日本数学会年会
    • Place of Presentation
      筑波大学 (茨城県つくば市)
    • Year and Date
      2016-03-19
    • Related Report
      2015 Research-status Report
  • [Presentation] Algebraic construction of integrable stochastic particle systems2015

    • Author(s)
      竹山 美宏
    • Organizer
      可積分系理論の諸分野への応用
    • Place of Presentation
      京都大学数理解析研究所 (京都府京都市)
    • Year and Date
      2015-08-21
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] A deformation of affine Hecke algebra and integrable stochastic particle system2015

    • Author(s)
      竹山美宏
    • Organizer
      日本数学会年会
    • Place of Presentation
      明治大学
    • Year and Date
      2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] Algebraic construction of integrable stochastic system2015

    • Author(s)
      竹山美宏
    • Organizer
      数学・物理における可積分性の諸相
    • Place of Presentation
      大阪市立大学
    • Year and Date
      2015-03-10
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] A deformation of affine Hecke algebra and integrable stochastic particle system2014

    • Author(s)
      Yoshihiro Takeyama
    • Organizer
      From Macdonald Processes to Hecke Algebras and Quantum Integrable Systems
    • Place of Presentation
      Institut Henri Poincare
    • Year and Date
      2014-05-28
    • Related Report
      2014 Research-status Report
    • Invited

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Published: 2014-04-04   Modified: 2019-03-29  

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