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Categorical study of representation theory of finite groups and algebras

Research Project

Project/Area Number 25400003
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

ODA Fumihito  近畿大学, 理工学部, 准教授 (00332007)

Project Period (FY) 2013-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordsバイセット関手 / バーンサイド環 / 一般バーンサイド環 / 対称群 / 二面体群 / 単元群 / バーンサイド関手 / 有限群 / マッキー関手 / グリーン関手 / 丹原関手 / 指標環 / 表現環 / ダブルバーンサイド環
Outline of Final Research Achievements

We showed that there is a relation between the unit element of the generalized Burnside ring of a symmetric group relative to the Young subgroups, the reduced Lefschetz module and the tom Dieck homomorphism. More precisely, we characterized a non-identity unit of the generalized Burnside ring of a symmetric group relative to the Young subgroups in terms of the tom Dieck homomorphism. Consequently, we have shown that the unit group of the ring is included in the image by the tom Dieck homomorphism. We have submitted to a paper of the result to a journal of mathematics.
We showed that the rank of the unit group of the generalized Burnside ring of a dihedral group relative to the parabolic subgroups is two. We have submitted to a paper of the result to a journal of mathematics.

Report

(4 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (14 results)

All 2015 2014 2013 Other

All Journal Article (9 results) (of which Acknowledgement Compliant: 5 results,  Peer Reviewed: 2 results) Presentation (5 results) (of which Invited: 4 results)

  • [Journal Article] The table of marks, the Kostka matrix, and the character table of the symmetric group2015

    • Author(s)
      小田文仁
    • Journal Title

      京都大学数理解析研

      Volume: 1965 Pages: 1-4

    • Related Report
      2015 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] 対称群の一般バーンサイド環のユニット元2015

    • Author(s)
      小田文仁
    • Journal Title

      第 60 回代数学シンポジウム報告集

      Volume: 60 Pages: 259-264

    • Related Report
      2015 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] The units of a partial Burnside ring relative to the Young subgroups of a symmetric group2015

    • Author(s)
      小田文仁、竹ヶ原裕元、吉田知行
    • Journal Title

      第 32 回代数的組合せ論シンポジウム報告集

      Volume: 32 Pages: 66-71

    • NAID

      120005838325

    • Related Report
      2015 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] グラフと有限群の再構成予想2015

    • Author(s)
      小田文仁、竹ヶ原裕元、吉田知行
    • Journal Title

      第 32 回代数的組合せ論シンポジウム報告集

      Volume: 32 Pages: 72-81

    • Related Report
      2015 Annual Research Report
    • Acknowledgement Compliant
  • [Journal Article] 有限群に関連した圏論的構成2015

    • Author(s)
      小田文仁、中岡宏行
    • Journal Title

      数学

      Volume: 67 Pages: 55-81

    • NAID

      130005733096

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] The table of marks, the Kostka matrix, and the character table of the symmetric group2015

    • Author(s)
      Hokuto Idei, Fumihito Oda
    • Journal Title

      Journal of Algebra

      Volume: 429 Pages: 318-323

    • DOI

      10.1016/j.jalgebra.2015.02.001

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] ON MULTIPLICATIVE INDUCTION2014

    • Author(s)
      小田文仁
    • Journal Title

      数理解析研究所講究録

      Volume: 1872 Pages: 151-158

    • Related Report
      2013 Research-status Report
  • [Journal Article] グリーン関手と有限群のドリンフェルトダブルの表現環2013

    • Author(s)
      小田文仁
    • Journal Title

      数理解析研究所講究録

      Volume: 1840 Pages: 122-128

    • Related Report
      2013 Research-status Report
  • [Journal Article] 丹原関手に関する注意2013

    • Author(s)
      小田文仁
    • Journal Title

      第29回代数的組合せ論シンポジウム報告集

      Volume: 1 Pages: 37-44

    • Related Report
      2013 Research-status Report
  • [Presentation] 対称群の一般バーンサイド環のユニット元2015

    • Author(s)
      小田文仁
    • Organizer
      第 60 回 代数学シンポジウム
    • Place of Presentation
      静岡大学共通教育A棟A201
    • Year and Date
      2015-09-03
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] The units of a partial Burnside ring relative to the Young subgroups of a symmetric group2015

    • Author(s)
      小田文仁
    • Organizer
      第 32 回代数的組合せ論シンポジウム
    • Place of Presentation
      石川県文教会館 401
    • Year and Date
      2015-06-24
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] 対称群のマーク行列, コストカ行列, 指標表2015

    • Author(s)
      小田文仁
    • Organizer
      2015の本数学会年会
    • Place of Presentation
      明 治 大 学 駿 河 台 キ ャ ン パ ス(東京都千代田区)
    • Year and Date
      2015-03-23
    • Related Report
      2014 Research-status Report
  • [Presentation] The generalized Burnside ring and the character ring of the symmetric group2014

    • Author(s)
      小田文仁
    • Organizer
      RIMS研究集会「有限群とその表現,頂点作用素代数,組合せ論の研究」
    • Place of Presentation
      京都大学数理解析研究所(京都府京都市)
    • Year and Date
      2014-12-16
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] バーンサイド環の乗法的誘導写像

    • Author(s)
      小田文仁
    • Organizer
      第25回有限群論草津セミナー
    • Place of Presentation
      草津セミナーハウス(群馬県)
    • Related Report
      2013 Research-status Report
    • Invited

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

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