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2010 Fiscal Year Self-evaluation Report

Macdonald polynomials, multivariable hypergeometric series and their application to lattice models

Research Project

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Project/Area Number 20540203
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionThe University of Tokyo

Principal Investigator

SHIRAISHI Junichi  The University of Tokyo, 大学院・数理科学研究科, 准教授 (20272536)

Project Period (FY) 2008 – 2011
Keywords可積分系
Research Abstract

A型のMacdonald多項式についてはPieri公式がよくわかっており、それによって明示的公式が導かれている。しかし、A型以外ののMacdonald多項式やKoornwinder多項式に対しては、Pieri公式の研究が十分には進められていないのが現状である。本研究の目的は、Macdonald多項式、Koornwinder多項式などの多変数の直交多項式の明示的公式を見いだすこと、量子群などの何らかの代数的構造を軸にして全体像を理解すること、及び、それらの知見を可解格子模型への応用することである。また、楕円関数を用いて定義されるRuijsenaars系に関しても理解を進めたい。

  • Research Products

    (8 results)

All 2010 2009 2008

All Journal Article (4 results) Presentation (4 results)

  • [Journal Article] Periodic Benjamin-Ono equation with discrete Laplacian and 2D-Toda Hierarchy,In New Trenda inQuantum Integrable Systems2010

    • Author(s)
      J.Shiraishi, Y.Tutiya
    • Journal Title

      Proceeding of the Infinite Analysis 09(Editors B.Feigin, M.Jimbo and M.Okado)(World Scientific)

      Pages: 357-371

  • [Journal Article] Periodic ILW equation with discrete Laplacian2009

    • Author(s)
      J.Shiraishi, Y.Tutiya
    • Journal Title

      J.Phys.A 42 no.40

      Pages: 15(404018)

  • [Journal Article] A commutative algebra on degenerate CP^1 and Macdonald polynomials2009

    • Author(s)
      B.Feigin, K.Hashizume, A.Hoshino, J.Shiraishi, S.Yanagida
    • Journal Title

      J.Math.Phys.50 no.9

      Pages: 42(095215)

  • [Journal Article] Kernel functions for difference operators of Ruijsenaars type and their applications.2009

    • Author(s)
      Y.Komori, M.Noumi, J.Shiraishi
    • Journal Title

      SIGMA Symmetry Integrability Geom.Methods Appl.5 054

      Pages: 40

  • [Presentation] 15th Itzykson meeting, Nwe trends in quantum integrability2010

    • Author(s)
      Macdonald polynomials and quantum algebras
    • Organizer
      IPhT Saclay
    • Place of Presentation
      France
    • Year and Date
      2010-06-23
  • [Presentation] Infinite Analysis 09, New Trends in Quantum Integrable Systems2009

    • Author(s)
      Hirota-Miwa equations, Macdonald operators
    • Organizer
      Department of Mathematics Kyoto University
    • Place of Presentation
      Japan
    • Year and Date
      2009-07-30
  • [Presentation] 日本数学会秋期総合分科会2008

    • Author(s)
      Macdonald多項式と可積分系
    • Place of Presentation
      東京工業大学(特別講演)
    • Year and Date
      2008-09-25
  • [Presentation] Workshop "Integrable quantum systems and solvable statistical mechanical models2008

    • Author(s)
      Macdonald polynomials and integrals of motion
    • Organizer
      CRM Centre de Recherches Math\'ematiques, Montreal
    • Place of Presentation
      Canada
    • Year and Date
      2008-07-04

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Published: 2012-02-13   Modified: 2016-04-21  

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