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Modular representations of algebraic groups

Research Project

Project/Area Number 23540023
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

KANEDA masaharu  大阪市立大学, 大学院・理学研究科, 教授 (60204575)

Co-Investigator(Renkei-kenkyūsha) TANISAKI Toshiyuki  大阪市立大学, 大学院理学研究科, 教授 (70142916)
YAGITA Nobuaki  茨城大学, 教育学部, 教授 (20130768)
TEZUKA Michishige  琉球大学, 理学部, 教授 (20197784)
FURUSAWA Masaaki  大阪市立大学, 大学院理学研究科, 教授 (50294525)
HASHIMOTO Yoshitake  東京都市大学, 知識工学部, 教授 (20271182)
KAWATA Shigeto  大阪市立大学, 大学院理学研究科, 准教授 (50195103)
Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords代数群 / modular表現 / Frobenius kernel / 量子群 / flag variety / cohomology / 代数群のmodular表現 / quadrics / G_1P-Verma modules / exceptional collection / reducitve group / parabolic induction / graded induction / Loewy series / rigidity / 国際研究者交流 仏蘭西 / Frobenius splitting / G_1T-Verma modules / 国際研究者交流 Australia / 国際情報交流 Denmark / G_1T-modules
Outline of Final Research Achievements

Let G be a reductive algebraic group over an algebraically closed field of positive characteristic p, P a parabolic subgroup of G, and T a maximal torus of P,
G_1 the Frobenius kernel of G. In joint work with Abe Noriyuki we determined the G_1T-structure of G_1P-Verma modules of p-regular highest weights for large p.
In joint work with H.H. Andersen we determined the cohomology vanishing behavior of line bundles on G/B in type G_2 when the corresponding B-modules lie in the lowest p^2-alcoves. In join work with M. Gros we constructed a Frobenius splitting on a quantum group at a root of unity.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (14 results)

All 2015 2014 2013 2012 2011 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results,  Open Access: 1 results,  Acknowledgement Compliant: 1 results) Presentation (7 results) (of which Invited: 3 results)

  • [Journal Article] Loewy series of parabolically induced G_1T-Verma modules2015

    • Author(s)
      Noriyuki Abe, Masaharu Kaneda
    • Journal Title

      Journal of the Institute of Mathematics of Jussieu

      Volume: 13 Issue: 1 Pages: 185-220

    • DOI

      10.1017/s1474748014000012

    • Related Report
      2014 Annual Research Report 2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Exceptional collections of sheaves on quadrics in positive characteristic2014

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

      Sao Paulo Journal of Mathematical Sciences

      Volume: 8

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] On a lemma of Samokhin2013

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

      Algebr. Represent. Theory

      Volume: 16 Issue: 4 Pages: 1159-1163

    • DOI

      10.1007/s10468-012-9350-6

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Contraction par Frobenius de $G$-modules2012

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

      Ann. Inst. Fourier (Grenoble)

      Volume: 61-6 Pages: 2507-2542

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Homomorphisms between neighboring $G_1T$-Verma modules2012

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

      Contemp. Math.

      Volume: 565 Pages: 105-113

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Cohomology of line bundles on the flag variety for type $G_2$2012

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

      Journal of Pure and Applied Algebra

      Volume: 216 Pages: 1566-1579

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Rigidity of tilting modules2011

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

      Moscow Mathematical Jpurnal

      Volume: 11 no.1 Pages: 1-39

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Graded G1T-parabolic induction2014

    • Author(s)
      Kaneda, M.
    • Organizer
      Workshop: Representations of algebraic groups
    • Place of Presentation
      University of Lyon, Lyon, France
    • Year and Date
      2014-07-04
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] On the structure of parabolically induced $G_1T$-Verma modules2012

    • Author(s)
      Kaneda, M*
    • Organizer
      Representation Theory of Chevalley Groups and Related Topics(招待講演)
    • Place of Presentation
      名古屋大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Geometry of the flag varieties and representation theory2011

    • Author(s)
      Kaneda, M.
    • Organizer
      談話会(招待講演)
    • Place of Presentation
      南京大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Frobenius splitting on $\Dist(G)$2011

    • Author(s)
      Kaneda, M*
    • Organizer
      談話会(招待講演)
    • Place of Presentation
      上海同済大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Geometry of the flag variety and $G_1T$-Verma modules2011

    • Author(s)
      Kaneda, M*
    • Organizer
      Univ. of Melbourne Algebra/Geometry/Topology Seminar(招待講演)
    • Place of Presentation
      University of Melbourne
    • Related Report
      2011 Research-status Report
  • [Presentation] A Frobenius splitting on the algebra of distributions

    • Author(s)
      Kaneda, M.
    • Organizer
      Algebra Seminar
    • Place of Presentation
      Universidade de Brasilia
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] On the Frobenius direct image of the structure sheaf of the flag variety

    • Author(s)
      Kaneda, M.
    • Organizer
      Algebra Seminar
    • Place of Presentation
      Sao Paulo University
    • Related Report
      2012 Research-status Report
    • Invited

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Published: 2011-08-05   Modified: 2019-07-29  

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