• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Research on Lie theory and representation theory of algebras

Research Project

Project/Area Number 15K04782
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Ariki Susumu  大阪大学, 情報科学研究科, 教授 (40212641)

Project Period (FY) 2015-04-01 – 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: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsヘッケ代数 / 表現型 / ヘッケ代数のブロック代数 / ブラウアー木代数 / 円分箙ヘッケ代数 / スぺヒト加群 / 古典型ヘッケ代数
Outline of Final Research Achievements

Hecke algebras are finite dimensional algebras which occupy an important position in Lie theory. Nowadays they are generalized to wider class of cyclotomic quiver Hecke algebras. In this research, we have studied the cyclotomic quiver Hecke algebras for affine type C aiming at contruction of Specht modules, in view of the fact that Specht modules play an important role in the representation theory of the cyclotomic Hecke algebras of affine type A. The research is successful and the results are in the preprint arXiv:1703.06425. Furthermore, assuming that the base field is algebraically closed of odd characteristic, we have not only determined the representation type of block algebras of Hecke algebras of classical type but also have dtermined the algebra structure of those of finite representation type. The reults are published as a refereed paper in a journal.

Report

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

    (18 results)

All 2017 2016 2015 Other

All Int'l Joint Research (1 results) Journal Article (5 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 5 results,  Acknowledgement Compliant: 2 results,  Open Access: 2 results) Presentation (9 results) (of which Int'l Joint Research: 6 results,  Invited: 9 results) Funded Workshop (3 results)

  • [Int'l Joint Research] University of Seoul(韓国)

    • Related Report
      2016 Research-status Report
  • [Journal Article] Representation type for block algebras of Hecke algebras of classical type2017

    • Author(s)
      Susumu Ariki
    • Journal Title

      Advances in Mathematics

      Volume: 317 Pages: 823-845

    • DOI

      10.1016/j.aim.2017.07.018

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On components of stable Auslander-Reiten quivers that contain Heller lattices: the case of truncated polynomial rings2017

    • Author(s)
      Susumu Ariki, Ryoichi Kase and Kengo Miyamoto
    • Journal Title

      Nagoya Math. J.

      Volume: 228 Pages: 72-113

    • DOI

      10.1017/nmj.2016.53

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Representation type of finite quiver Hecke algebras of type D^{(2)}_{l+1}2016

    • Author(s)
      Susumu Ariki and Euiyong Park
    • Journal Title

      Trans. Amer. Math. Soc.

      Volume: 368 Issue: 5 Pages: 3211-3242

    • DOI

      10.1090/tran/6411

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Representation type of finite quiver Hecke algebras of type C^{(1)}_l2016

    • Author(s)
      Susumu Ariki and Euiyong Park
    • Journal Title

      Osaka J. Math.

      Volume: 53 Pages: 463-488

    • NAID

      120005941442

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Representation type of finite quiver Hecke algebras of type A^{(1)}_l for arbitrary parameters2015

    • Author(s)
      S. Ariki, K. Iijima, E. Park
    • Journal Title

      Int. Math. Res. Not.

      Volume: IMRN2015, no.15 Issue: 15 Pages: 6070-6135

    • DOI

      10.1093/imrn/rnu115

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] 組合せ論的表現論への入門I, II2017

    • Author(s)
      有木進
    • Organizer
      代数学若手研究会
    • Place of Presentation
      岡山大学
    • Year and Date
      2017-03-07
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] On block algebras of Hecke algebras of classical type2017

    • Author(s)
      Susumu Ariki
    • Organizer
      Representation Theory of Symmetric Groups and Related Algebras
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Block algebras of Hecke algebras of classical type2017

    • Author(s)
      Susumu Ariki
    • Organizer
      Conference on Algebraic Representation Theory
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Representation type for block algebras of Hecke algebras2016

    • Author(s)
      Susumu Ariki
    • Organizer
      Conference on Algebraic Representation Theory
    • Place of Presentation
      Harbin Institute of Technology, Shenzhen, P.R.China
    • Year and Date
      2016-12-04
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Heller lattices and AR quivers2016

    • Author(s)
      Susumu Ariki
    • Organizer
      International Conference for KMS 70th Anniversary
    • Place of Presentation
      ソウル国立大学、ソウル、大韓民国
    • Year and Date
      2016-10-22
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Representation type for block algebras of Hecke algebras2016

    • Author(s)
      Susumu Ariki
    • Organizer
      Geometric Representation Theory
    • Place of Presentation
      京都大学
    • Year and Date
      2016-10-14
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Rouquier’s theory of quasi-hereditary covers I, II2016

    • Author(s)
      Susumu Ariki
    • Organizer
      Summer School on Quasi-hereditary Algebras
    • Place of Presentation
      大阪府立大学
    • Year and Date
      2016-08-29
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Symmetric algebras arising from categorification of integrable modules I, II2015

    • Author(s)
      S.Ariki
    • Organizer
      第48回環論および表現論シンポジウム
    • Place of Presentation
      静岡大学
    • Year and Date
      2015-09-07
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] Combinatroics of Hecke algebras2015

    • Author(s)
      S.Ariki
    • Organizer
      Formal Power Series and Algebraic Combinatorics
    • Place of Presentation
      KAIST, Daejeon, Korea
    • Year and Date
      2015-07-10
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Funded Workshop] Conference on Algebraic Representation Theory2017

    • Related Report
      2017 Annual Research Report
  • [Funded Workshop] Conference on Algebraic Representation Theory2016

    • Place of Presentation
      Harbin Institute of Technology, Shenzhen
    • Year and Date
      2016-12-02
    • Related Report
      2016 Research-status Report
  • [Funded Workshop] Shanghai Conference on Representation Theory2015

    • Place of Presentation
      Tian He Hotel, Chongming Island, Shanghai
    • Year and Date
      2015-12-07
    • Related Report
      2015 Research-status Report

URL: 

Published: 2015-04-16   Modified: 2022-02-16  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi