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Multivariate orthogonal polynomials on finite groups and their q-analogues

Research Project

Project/Area Number 21740032
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research Institution防衛大学校

Principal Investigator

MIZUKAWA Hiroshi  防衛大学校, 総合教育学群, 准教授 (60531762)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords表現論 / 代数的組合せ論 / 球関数 / 超幾何関数 / ヘッケ環 / q-超幾何関数 / ヘッケ代数 / ゲルファントペア / 半正規表現 / 多変数直交多項式 / シュバレー群 / 代数統計学 / 帯球関数 / 直交多項式 / 対称関数 / 代数群 / 代数的統計学
Research Abstract

In this study, I dealt with the special functions arising from finite groups or their q-analogues. As results, I obtained the complete description of the spherical functions of a certain Gelfand pair which is generalization of the Gelfand pair(S_2n, H_n), a necessary and sufficient condition of orthogonal properties of multivariate Krawtchouk polynomials, and a formulae of the character of the symmetric groups. Furthermore I applied these results on finite homogenous spaces as stochastic spaces and obtained a generalization of classical Frobenius-Schur theorem.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (25 results)

All 2011 2010 2009 Other

All Journal Article (11 results) (of which Peer Reviewed: 5 results) Presentation (12 results) Book (2 results)

  • [Journal Article] Wreath product generalizations of the triple(S_2n, H_n,φ) and their spherical functions2011

    • Author(s)
      Hiroshi Mizukawa
    • Journal Title

      J. Alg

      Volume: 334 Pages: 31-53

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Twisted Gelfand pair of complex reflection groups and r-congruence properties of Schur functions2011

    • Author(s)
      Hiroshi Mizukawa
    • Journal Title

      Ann. Comb

      Volume: 15 Pages: 119-125

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Orthogonality relations for multivariate Krawtchouk polynomials2011

    • Author(s)
      Hiroshi Mizukawa
    • Journal Title

      SIGMA

      Volume: 7 Pages: 17-17

    • URL

      http://dx.doi.org/10.3842/SIGMA.2011.01

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Wreath product generalizations of the triple $(S_{2n},H_n,¥varphi)$ and their spherical functions2011

    • Author(s)
      水川裕司
    • Journal Title

      Journal of Algebra

      Volume: 334 Issue: 1 Pages: 31-53

    • DOI

      10.1016/j.jalgebra.2011.02.036

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Twisted Gelfand pairs of complex refrection groups and r-congruence properties of Schur functions2011

    • Author(s)
      Hiroshi Mizukawa
    • Journal Title

      Annals of Combunatorics

      Volume: 15 Pages: 119-125

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] フロベニウス=シューアの定理とその一般化2010

    • Author(s)
      水川裕司
    • Journal Title

      数理解析研究所講究録

      Volume: 1687 Pages: 167-173

    • Related Report
      2011 Final Research Report
  • [Journal Article] 有限等質空間の調和解析と統計に関する話題2010

    • Author(s)
      水川裕司
    • Journal Title

      数理解析研究所講究録

      Volume: 1593 Pages: 190-196

    • Related Report
      2011 Final Research Report
  • [Journal Article] 有限群上の調和解析2010

    • Author(s)
      水川裕司
    • Journal Title

      第54回代数学シンポジウム報告集

      Pages: 223-244

    • Related Report
      2011 Final Research Report
  • [Journal Article] 有限群上の調和解析と統計学に関する話題2010

    • Author(s)
      水川裕司
    • Journal Title

      数理解析研究所講究録「表現論と組合せ論」

      Volume: 1689 Pages: 153-163

    • Related Report
      2010 Annual Research Report
  • [Journal Article] フロベニウス=シューアの定理の一般化とその応用2010

    • Author(s)
      水川裕司
    • Journal Title

      数理解析研究所講究録「代数的組合せ論および関連する群と代数」

      Volume: 1687 Pages: 167-173

    • Related Report
      2010 Annual Research Report
  • [Journal Article] 有限群上の調和解析2010

    • Author(s)
      水川裕司
    • Journal Title

      第54回 代数学シンポジウム報告集

      Volume: 第54回 Pages: 233-243

    • Related Report
      2010 Annual Research Report
  • [Presentation] 壺とボールの有限群論的解釈2010

    • Author(s)
      水川裕司
    • Organizer
      科研費研究集会「計算代数と数理統計学の新たな展開
    • Place of Presentation
      ソニックシティ大宮(埼玉県)
    • Year and Date
      2010-11-15
    • Related Report
      2011 Final Research Report
  • [Presentation] つぼとボールの有限群論的解釈2010

    • Author(s)
      水川裕司
    • Organizer
      科研費集会「計算代数と数理統計学の新たな展開」
    • Place of Presentation
      大宮ソニックシティ(さいたま市)
    • Year and Date
      2010-11-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] 有限群のGelfand pairの壺とボールのモデルへの応用2010

    • Author(s)
      水川裕司
    • Organizer
      日本数学会秋季総合文科会
    • Place of Presentation
      名古屋大学(愛知県)
    • Year and Date
      2010-09-24
    • Related Report
      2011 Final Research Report
  • [Presentation] 有限群のGelfand Pairの壷とボールのモデルへの応用2010

    • Author(s)
      水川裕司
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      名古屋大学(名古屋市)
    • Year and Date
      2010-09-24
    • Related Report
      2010 Annual Research Report
  • [Presentation] ロベニウス=シューアの定理の一般化とその応用2009

    • Author(s)
      水川裕司
    • Organizer
      RIMS研究集会「代数的組合せ論および関連する群と代数
    • Place of Presentation
      信州大学(長野県)
    • Year and Date
      2009-11-20
    • Related Report
      2011 Final Research Report
  • [Presentation] フロベニウスーシューアの定理の一般化とその応用2009

    • Author(s)
      水川裕司
    • Organizer
      RIMS研究集会「代数的組合せ論および関連する群と代数」
    • Place of Presentation
      信州大学(松本市)
    • Year and Date
      2009-11-20
    • Related Report
      2009 Annual Research Report
  • [Presentation] ブラウアー・シューア函数2009

    • Author(s)
      青影一哉、水川裕司、山田裕史
    • Organizer
      2009年度表現論シンポジウム
    • Place of Presentation
      健康文化村(宜野湾市)
    • Year and Date
      2009-11-18
    • Related Report
      2009 Annual Research Report
  • [Presentation] 有限群の既約指標と共役類に関する公式2009

    • Author(s)
      水川裕司
    • Organizer
      第8回組合せ論サマースクール
    • Place of Presentation
      稚内北星学園大学(北海道)
    • Year and Date
      2009-09-01
    • Related Report
      2011 Final Research Report
  • [Presentation] 有限群の既約指標と共役類に関する公式2009

    • Author(s)
      水川裕司
    • Organizer
      組合せサマースクール2009
    • Place of Presentation
      稚内北星学園大学(稚内市)
    • Year and Date
      2009-09-01
    • Related Report
      2009 Annual Research Report
  • [Presentation] 有限群上の調和解析と統計に関する話題2009

    • Author(s)
      水川裕司
    • Organizer
      RIMS研究集会「表現論と組合せ論」
    • Place of Presentation
      北海道大学(北海道)
    • Year and Date
      2009-08-28
    • Related Report
      2011 Final Research Report
  • [Presentation] 有限群上の調和解析と統計学に関する話題2009

    • Author(s)
      水川裕司
    • Organizer
      RIMS研究集会「表現論と組合せ論」
    • Place of Presentation
      北海道大学(札幌市)
    • Year and Date
      2009-08-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] 有限群上の調和解析2009

    • Author(s)
      水川裕司
    • Organizer
      第54回代数学シンポジウム
    • Place of Presentation
      明治大学(東京都)
    • Year and Date
      2009-08-06
    • Related Report
      2011 Final Research Report 2009 Annual Research Report
  • [Book] QUANTIZED ALGEBRA AND PHYSICS2011

    • Author(s)
      Mo-Lin Ge, et.al.(編)
    • Publisher
      World Scientific Pub Co Inc
    • Related Report
      2011 Annual Research Report
  • [Book] UANTIZED ALGEBRA AND PHYSICS Proceeding of the International Workshop

    • Author(s)
      Mo-Lin Ge
    • Total Pages
      210
    • Publisher
      World Scientific Co Pub
    • URL

      http://www.worldscibooks.com/mathematics/8081.html

    • Related Report
      2011 Final Research Report

URL: 

Published: 2009-04-01   Modified: 2016-04-21  

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