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Research on the difference systems associated with multivariable elliptic hypergeometric functions with Weyl group symmetry

Research Project

Project/Area Number 25400118
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionUniversity of the Ryukyus (2017)
Tokyo Denki University (2013-2016)

Principal Investigator

ITO Masahiko  琉球大学, 理学部, 教授 (30348461)

Co-Investigator(Renkei-kenkyūsha) NOUMI Masatoshi  神戸大学, 理学研究科, 教授 (80164672)
OKADA Soichi  名古屋大学, 多元数理科学研究科, 教授 (20224016)
KANEKO Jouichi  琉球大学, 理学部, 教授 (10194911)
Research Collaborator FORRESTER Peter J.  メルボルン大, 理学部, 教授
Project Period (FY) 2013-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywords楕円超幾何関数 / 楕円セルバーグ積分 / 楕円ガンマ関数 / 楕円補間関数 / ワイル群対称性 / 差分方程式系 / マクドナルド定数項恒等式 / 補間関数 / Macdonald定数項恒等式 / G2型Weyl群 / 楕円超幾何級数 / 接続公式 / Sears-Slater 変換 / Gustafson-Rakha の和公式 / Askey-Wilson 積分 / Dixon-Anderson 積分 / 既約指標 / シルベスター行列式
Outline of Final Research Achievements

The multivariable elliptic hypergeometric functions associated with root systems were studied via their systems of difference equations and Weyl group symmetry. Masahiko Ito (the leader of this research, Univ. of the Ryukyus) and Masatoshi Noumi (cooperating researcher of this research, Kobe univ.) provided a definition of the family of ``interpolation functions'' for the multivariable elliptic hypergeometric functions of type BCn. This is the main result of this research. As applications of the interpolation functions, several summation and translation formulae for the multivariable elliptic hypergeometric functions of type BCn were proved.

Report

(6 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (19 results)

All 2018 2017 2016 2015 2014 2013 Other

All Int'l Joint Research (1 results) Journal Article (8 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 8 results,  Open Access: 3 results,  Acknowledgement Compliant: 4 results) Presentation (10 results) (of which Int'l Joint Research: 1 results,  Invited: 1 results)

  • [Int'l Joint Research] メルボルン大学(オーストラリア)

    • Related Report
      2017 Annual Research Report
  • [Journal Article] A bilateral extension of the q-Selberg integral2017

    • Author(s)
      Masahiko Ito, Peter J. Forrester
    • Journal Title

      Transactions of the American Mathematical Society

      Volume: 369 Issue: 4 Pages: 2843-2878

    • DOI

      10.1090/tran/6851

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Evaluation of the $BC_n$ elliptic Selberg integral via the fundamental invariants2017

    • Author(s)
      M. Ito, M. Noumi
    • Journal Title

      Proc. Amer. Math. Soc.

      Volume: 145 Issue: 2 Pages: 689-703

    • DOI

      10.1090/proc/13234

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A generalization of the Sears--Slater transformation and elliptic Lagrange interpolation of type $BC_n$2016

    • Author(s)
      M. Ito, M. Noumi
    • Journal Title

      Adv. in Math.

      Volume: 229 Pages: 361-380

    • DOI

      10.1016/j.aim.2016.05.016

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Derivation of a BCn elliptic summation formmula via the fundamental invariants2016

    • Author(s)
      M. Ito and M. Noumi
    • Journal Title

      Constr. Approx.

      Volume: 未定 Issue: 1 Pages: 33-46

    • DOI

      10.1007/s00365-016-9340-8

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] On a family of integrals that extend the Askey-Wilson integral2015

    • Author(s)
      Masahiko Ito, N.S. Witte
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 421 Issue: 2 Pages: 1101-1130

    • DOI

      10.1016/j.jmaa.2014.07.056

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The q-Dixon-Anderson integral and multi-dimensional 1ψ1 summations2015

    • Author(s)
      Masahiko Ito, Peter J. Forrester
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 423 Issue: 2 Pages: 1704-1737

    • DOI

      10.1016/j.jmaa.2014.10.034

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Ramanujan's 1ψ1 summation theorem ―perspective, announcement of bilateral q-Dixon-Anderson and q-Selberg integral extensions, and context―2014

    • Author(s)
      Masahiko Ito, Peter J. Forrester
    • Journal Title

      Proceedings of the Japan Academy, Series A, Mathematical Sciences

      Volume: 90 Issue: 7

    • DOI

      10.3792/pjaa.90.92

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A compound determinant identity for rectangular matrices and determinants of Schur functions2013

    • Author(s)
      M. Ishikawa, M. Ito, and S. Okada
    • Journal Title

      Advances in Applied Mathematics

      Volume: 51 Issue: 5 Pages: 635-654

    • DOI

      10.1016/j.aam.2013.08.001

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] G2型Weyl群不変なq超幾何積分の行列式公式2018

    • Author(s)
      伊藤雅彦 宮永愛子 野海正俊
    • Organizer
      日本数学会年会「無限可積分系セッション」(東京大学)
    • Related Report
      2017 Annual Research Report
  • [Presentation] A determinant formula associated with the elliptic hypergeometric integrals of type BCn2017

    • Author(s)
      Masahiko Ito
    • Organizer
      Elliptic Hypergeometric Functions in Combinatorics, Integrable Systems and Physics
    • Place of Presentation
      ウィーン大学エルヴィン・シュレーディンガー研究所(オーストリア、ウィーン)
    • Year and Date
      2017-03-23
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Selberg型BCn楕円超幾何積分の行列式公式2017

    • Author(s)
      伊藤雅彦 野海正俊
    • Organizer
      日本数学会秋季総合分科会「無限可積分系セッション」(山形大学)
    • Related Report
      2017 Annual Research Report
  • [Presentation] Gustafson-Rakha 和公式の楕円化2016

    • Author(s)
      伊藤雅彦 野海正俊
    • Organizer
      日本数学会秋季総合分科会「無限可積分系セッション」
    • Place of Presentation
      関西大学(大阪府、吹田市)
    • Year and Date
      2016-09-15
    • Related Report
      2016 Research-status Report
  • [Presentation] A型 Jackson 積分と Ramanujan 1ψ1 和公式, Slater rψr 変換公式の一般化2016

    • Author(s)
      伊藤雅彦 野海正俊
    • Organizer
      日本数学会2016年度年会「無限可積分系セッション」
    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Year and Date
      2016-03-18
    • Related Report
      2015 Research-status Report
  • [Presentation] A型楕円Lagrange補間函数の構成法2016

    • Author(s)
      伊藤雅彦 野海正俊
    • Organizer
      日本数学会2016年度年会「無限可積分系セッション」
    • Place of Presentation
      筑波大学(茨城県つくば市)
    • Year and Date
      2016-03-18
    • Related Report
      2015 Research-status Report
  • [Presentation] Sears-Slater の変換公式の一般化と BCn 型楕円 Lagrange 補間函数2015

    • Author(s)
      伊藤雅彦 野海正俊
    • Organizer
      日本数学会2015年度秋季総合分科会「無限可積分系セッション」
    • Place of Presentation
      京都産業大(京都府京都市)
    • Year and Date
      2015-09-14
    • Related Report
      2015 Research-status Report
  • [Presentation] BC型楕円多重和公式の基本不変式による導出2015

    • Author(s)
      伊藤雅彦 野海正俊
    • Organizer
      日本数学会2015年度年会「無限可積分系セッション」
    • Place of Presentation
      明治大学 駿河台キャンパス
    • Year and Date
      2015-03-23
    • Related Report
      2014 Research-status Report
  • [Presentation] q-Dixon-Anderson積分

    • Author(s)
      伊藤雅彦
    • Organizer
      日本数学会秋期分科会「無限可積分系セッション」
    • Place of Presentation
      愛媛大学(愛媛県)
    • Related Report
      2013 Research-status Report
  • [Presentation] 両側級数に拡張されたq-Selberg積分

    • Author(s)
      伊藤雅彦
    • Organizer
      日本数学会秋期分科会「無限可積分系セッション」
    • Place of Presentation
      愛媛大学(愛媛県)
    • Related Report
      2013 Research-status Report

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Published: 2014-07-25   Modified: 2019-07-29  

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