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Modular Representation Theory of General Linear Groups

Research Project

Project/Area Number 19740011
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

MIYACHI Hyohe  Nagoya University, 大学院・多元数理科学研究科, 助教 (90362227)

Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,830,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywords代数学 / 表現論 / 表現諭
Research Abstract

We studied representation theory of general linear groups in positive characteristic and quantum groups at roots of unity by a standard method such as treating different ranks, a rather standard method such as treating those groups at the same time and our new method that we change the "quantum characteristics" and we compare their module categories. Here, the speciality of our approach is to start with a very special category and then to pass it in the derived categories so that we are able to compare general module categories.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (17 results)

All 2010 2009 2008 Other

All Journal Article (9 results) (of which Peer Reviewed: 8 results) Presentation (6 results) Remarks (2 results)

  • [Journal Article] Runner Removal Morita Equivalences2010

    • Author(s)
      J. Chuang - 宮地兵衛
    • Journal Title

      Progress in Mathematics(Gyoja,A.;Nakajima,H.;Shinoda,K-i.;Shoji,T;Tanisaki,T.(Eds.)) Vol.284

      Pages: 450-450

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Module correspondences in Rouquier blocks of finite general linear groups2010

    • Author(s)
      飛田明彦 - 宮地兵衛
    • Journal Title

      Progress in Mathematics Vol.284

      Pages: 450-450

    • Related Report
      2009 Final Research Report
  • [Journal Article] Runner Removal Morita Equivalences2010

    • Author(s)
      J.Chuang-宮地兵衛
    • Journal Title

      Progress in Mathematics 284((受理))

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Module correspondences in Rouquier blocks of finite general linear groups2010

    • Author(s)
      飛田明彦, 宮地兵衛
    • Journal Title

      Progress in Mathematics 284((受理))

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uno's conjecture for the exceptional Iwahori-Hecke algebras. New trends in combinatorial representation theory2009

    • Author(s)
      宮地兵衛
    • Journal Title

      RIMS Kokyuroku Bessatsu, B11, Res. Inst. Math. Sci. (RIMS), Kyoto

      Pages: 155-177

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Rouquier blocks in Chevalley groups of type2008

    • Author(s)
      宮地兵衛
    • Journal Title

      E. Adv. Math. 217no.6

      Pages: 2841-2871

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Kleshchev's decomposition numbers and branching coefficients in the Fock space2008

    • Author(s)
      宮地兵衛
    • Journal Title

      Trans. Amer. Math. Soc. 360

      Pages: 1179-1191

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rouquier blocks in Chevalley groups of type E2008

    • Author(s)
      宮地兵衛
    • Journal Title

      Adv. Math. 217

      Pages: 2841-2871

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Rouquier blocks in Chevalley groups of type E2008

    • Author(s)
      Hyohe Miyachi
    • Journal Title

      Adv. Math. 217

      Pages: 2841-2871

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Comparing finite dimensional module categories over quantum general linear groups at different roots of unity2009

    • Author(s)
      宮地兵衛
    • Organizer
      代数的三角圏とその周辺
    • Place of Presentation
      京都大学
    • Year and Date
      2009-07-22
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] Dipper's hypothesis and selfinjective endomorphism rings2009

    • Author(s)
      宮地兵衛
    • Organizer
      Representations of Finite Groups
    • Place of Presentation
      MFO Oberwolfach, Germany
    • Year and Date
      2009-03-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] On an equivalence between the category O over a certain rational Cherednik algebra and a module category of a cyclotomic Schur algebra2009

    • Author(s)
      宮地兵衛
    • Organizer
      Workshop on Representation Theory and Complex Analysis
    • Place of Presentation
      Tongi University China
    • Related Report
      2009 Final Research Report
  • [Presentation] Dipper's hypothesis and selfinjective endomorphism rings2009

    • Author(s)
      宮地兵衛
    • Organizer
      Representations of Finite Groups, Mathematisches Forschungsinstitut Oberwolfach
    • Place of Presentation
      Oberwolfach, Germany
    • Related Report
      2009 Final Research Report
  • [Presentation] Irreducible Specht modules2008

    • Author(s)
      宮地兵衛
    • Organizer
      Workshop on Representation Theory and Complex Analysis
    • Place of Presentation
      Tongi University China
    • Related Report
      2009 Final Research Report
  • [Presentation] Equating decomposition numbers in different weights2008

    • Author(s)
      宮地兵衛
    • Organizer
      Workshop on Algebras in Lie Theory
    • Place of Presentation
      東京大学
    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://www.math.nagoya-u.ac.jp/~miyachi/index.html

    • Related Report
      2009 Final Research Report
  • [Remarks]

    • URL

      http://www.math.nagoya-u.ac.jp/~miyachi/index.html

    • Related Report
      2009 Annual Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

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