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2013 Fiscal Year Final Research Report

Graded Hecke algebras and quasihereditary covers

Research Project

  • PDF
Project/Area Number 23340006
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
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)

Co-Investigator(Renkei-kenkyūsha) TANISAKI Toshiyuki  大阪市立大学, 理学研究科, 教授 (70142916)
KANEDA Masaharu  大阪市立大学, 理学研究科, 教授 (60204575)
Project Period (FY) 2011-04-01 – 2014-03-31
Keywords圏化 / 箙ヘッケ代数
Research Abstract

We studied representation theory of graded Hecke algebras which are called quiver Hecke algebras. The quiver Hecke algebras were introduced for the purpose of categorifying integrable modules over quantum groups. In the early stage of the research, we proved certain nonnegativity result which was a property necessary to hold when we speak of categorification of Fock spaces. After that stage, we focused on categorification of basic modules over quantum groups of affine type. We were only able to handle the affine type A for long time. In the current research, we have succeeded in handling other affine types than affine type A and we have proved Erdmann-Nakano type theorems for finite quiver Hecke algebras. In particular, it allowed us to analyze finite quiver Hecke algebras of tame representation type in detail. Related to this analysis, we have classified two point symmetric special biserial algebras.

  • Research Products

    (14 results)

All 2014 2013 2012 2011 Other

All Journal Article (11 results) (of which Peer Reviewed: 11 results) Presentation (3 results)

  • [Journal Article] Representation type of finite quiver Hecke algebras of type A^{(2)}_{2l}2014

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

      J. Algebra

      Volume: 397卷 Pages: 457-488

    • Peer Reviewed
  • [Journal Article] On a lemma of Samokhin2013

    • Author(s)
      M. Kaneda
    • Journal Title

      Algebr. Represent. Theory

      Volume: 16卷 Pages: 1159-1163

    • Peer Reviewed
  • [Journal Article] Manin triples and differential operators on quantum groups2013

    • Author(s)
      T. Tanisaki
    • Journal Title

      Tokyo J. Math

      Volume: 36卷 Pages: 49-83

    • Peer Reviewed
  • [Journal Article] Cohomology of line bundles on the flag variety for type G22012

    • Author(s)
      H. Andersen, M. Kaneda
    • Journal Title

      J. Pure Appl. Algebra

      Volume: 216卷 Pages: 1566-1579

    • Peer Reviewed
  • [Journal Article] Homomorphisms between neighboring G1T-Verma modules, Algebraic groups and quantum groups2012

    • Author(s)
      M. Kaneda
    • Journal Title

      Contemp. Math

      Volume: 565卷 Pages: 105-113

    • Peer Reviewed
  • [Journal Article] D-modules and representation theory, Lie theory and representation theory2012

    • Author(s)
      T. Tanisaki
    • Journal Title

      Surv. Mod. Math

      Volume: 2卷 Pages: 177-219

    • Peer Reviewed
  • [Journal Article] Differential operators on quantized flag manifolds at roots of unity2012

    • Author(s)
      T. Tanisaki
    • Journal Title

      Adv. Math

      Volume: 230卷 Pages: 2235-2294

    • Peer Reviewed
  • [Journal Article] The modular branching rule for affine Hecke algebras of type A2011

    • Author(s)
      S. Ariki, N. Jacon, C. Lecouvey
    • Journal Title

      Adv. Math

      Volume: 228卷 Pages: 481-526

    • Peer Reviewed
  • [Journal Article] Contraction par Frobenius de G-modules2011

    • Author(s)
      M. Gros, M. Kaneda
    • Journal Title

      Ann. Inst. Fourier

      Volume: 61卷 Pages: 2507-2542

    • Peer Reviewed
  • [Journal Article] Rigidity of tilting modules2011

    • Author(s)
      H. Andersen, M. Kaneda
    • Journal Title

      Mosc. Math. J

      Volume: 11卷 Pages: 1-39, 181

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

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

      Trans. Amer. Math. Soc

      Volume: (掲載決定済)

    • Peer Reviewed
  • [Presentation] On the representation type and other properties of finite quiver Hecke algebras2013

    • Author(s)
      S. Ariki
    • Organizer
      Shanghai Workshop on Represent. Theory
    • Year and Date
      2013-12-08
  • [Presentation] Constructing a q.h. cover of a cellular algebra2012

    • Author(s)
      S. Ariki
    • Organizer
      Mini-Workshop on Comb. Represent. Theory
    • Place of Presentation
      Morningside Center, 中国科学院
    • Year and Date
      2012-06-11
  • [Presentation] Q.h. covers of Hecke algebras of type B22011

    • Author(s)
      S. Ariki
    • Organizer
      Modular Representations of Sym. Groups and Related Objects
    • Place of Presentation
      Oberwolfach 数学研究所
    • Year and Date
      2011-04-27

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Published: 2015-06-25  

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