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A Study on Derived Equivalences of Blocks and Shintani Descent in Group Algebras

Research Project

Project/Area Number 16540001
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHokkaido University of Education

Principal Investigator

OKUYAMA Tetsuro  Hokkaido University of Education, Faculty of Education, Professor, 教育学部旭川校, 教授 (60128733)

Co-Investigator(Kenkyū-buntansha) HASEGAWA Izumi  Hokkaido University of Education, Faculty of Education, Professor, 教育学部札幌校, 教授 (50002473)
KOMURO Naoto  Hokkaido University of Education, Faculty of Education, Professor, 教育学部旭川校, 教授 (30195862)
YATSUI Tomoaki  Hokkaido University of Education, Faculty of Education, Associate Professor, 教育学部旭川校, 助教授 (00261371)
KITAYAMA Masashi  Hokkaido University of Education, Faculty of Education, Professor, 教育学部釧路校, 教授 (80169888)
IAI Shin-ichiro  Hokkaido University of Education, Faculty of Education, Associate Professor, 教育学部札幌校, 助教授 (50333125)
福井 昌樹  北海道教育大学, 教育学部・旭川校, 教授 (20002628)
阿部 修  北海道教育大学, 教育学部・旭川校, 助教授 (30202659)
Project Period (FY) 2004 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥3,500,000 (Direct Cost: ¥3,500,000)
Fiscal Year 2005: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2004: ¥1,900,000 (Direct Cost: ¥1,900,000)
KeywordsRepresentations of Finite Groups / Block Algebras / Splendid Tilting Complexes / Shintani Descent / Broue's Conjecture
Research Abstract

In the research of this project, we studied "the abelian defect conjecture" which is one of main problems in representation theory of finite groups. We were concerned with Shintani descent and Glauberman correspondent.
1.We have constructed one sided tilting complexes for finite Chevalley groups of small rank, for example, U(3,q^2)、Sp(4,q)、G_2(q). We could construct Splendid tilting complexes which coincide with these complexes as one side complexes and studied perfect isometries between character rings induced by them.
2.The situations described in 1 can be considered problems of derived category version of "Glauberman correspondent". We have studied solvable group case and obtain some generalization of results by Harris and Linckelmann. And we clarify the strategy raised by Rouquier in this setting.
3.We also worked on a problem giving quiver presentations for various types of 5-Sylow normalizers of rank 2 to apply for constructing tilting complexes of some finite Chevalley groups, for example, ^2F_4(q) of which 5-Sylow normalizer is of 4S_4-type.

Report

(3 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • Research Products

    (21 results)

All 2006 2005 2004

All Journal Article (21 results)

  • [Journal Article] On a theorem of Mislin on cohomology isomorphism and control of fusion2006

    • Author(s)
      T.Okuyama
    • Journal Title

      数理解析研究所講究録 1466

      Pages: 86-92

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Annual Research Report 2005 Final Research Report Summary
  • [Journal Article] On a theorem of Mislin on cohomology isomorphism and control of fusion2006

    • Author(s)
      T.Okuyama
    • Journal Title

      Research Inst. for Math.Sci.Kokyuroku 1466

      Pages: 86-92

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Gorenstein graded rings associated to ideals2006

    • Author(s)
      S.Goto, S.-i.Iai
    • Journal Title

      Journal of Algebra (掲載予定)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Gorenstein graded rings associated to ideals2005

    • Author(s)
      S.Goto, S.-i.Iai
    • Journal Title

      Journal of Algebra 294

      Pages: 373-407

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Subspaces given by a projective Randers changedeals in regular local rings2005

    • Author(s)
      M.Kitayama
    • Journal Title

      Tensor N.S. 66

      Pages: 185-196

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Infinitesimal holomorphically projective transformations on tangent bundles with complete lift connections2005

    • Author(s)
      I.Hasegawa, K.Yamauchi
    • Journal Title

      Differential Geometry Dynamical Systens 7

      Pages: 42-48

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Facial structures of convex sets in Banach spaces and integrand representation of convex operators2005

    • Author(s)
      N.Komuro
    • Journal Title

      Taiwanese Journal of Mathematics 9

      Pages: 501-510

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Parabolic geometries associated with differential equations of finite type2005

    • Author(s)
      K.Yamaguchi, T.Yatsui
    • Journal Title

      Hokkaido University Preprint Series in Mathematics Series #756(to appear)

    • NAID

      120006459462

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Subspaces given by a projective Randers change2005

    • Author(s)
      M.Kiyayama
    • Journal Title

      Tehsor N.S. 66

      Pages: 185-196

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Infinitesimal holomorphically projectice transformation on tnagent bundles with complete lift2005

    • Author(s)
      I.Hasegawa, K.Yamaguchi
    • Journal Title

      Differential Geometry-Dynamical Systems 7

      Pages: 42-48

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Facial structure of convex sets in Banach spaces and integrand representations of convex operators2005

    • Author(s)
      N.Komuro
    • Journal Title

      Taiwanese Journal of Mathematics 9

      Pages: 501-510

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Parabolic geometries associated with differential equations of finite type2005

    • Author(s)
      T.Yatsui
    • Journal Title

      Hokkaido Univ.Preprint Series in Math. 756 (to appear)

    • NAID

      120006459462

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Infinitesimal holomorphically projective transformations on tangent bundles with complete lift connection2005

    • Author(s)
      I.Hasegawa, K.Yamauchi
    • Journal Title

      Differential Geometry Dynamical Systems 7

      Pages: 42-48

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Subspaces given by projective Randers change2005

    • Author(s)
      M.Kitayama
    • Journal Title

      Tensor, N.S 66-2

      Pages: 185-196

    • NAID

      10016688972

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Hypersurfaces given by a projective Randers change2005

    • Author(s)
      M.Kitayama, T.Tani
    • Journal Title

      Proceedings of International Workshop Applied Mathematics, Banat's University, Romania,

      Pages: 156-171

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Facial structure of convex sets in Banach spaces and integrand representation of convex operators2005

    • Author(s)
      N.Komuro
    • Journal Title

      Taiwanese Journal of Mathematics 9-3

      Pages: 501-510

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Subspaces given by a projective Randers change2005

    • Author(s)
      M.Kitayama
    • Journal Title

      Tensor, N.S. 66・1-2(掲載予定)

    • NAID

      10016688972

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Infinitesimal holomorphically projective transformations on Tangent bundles with complete lift connection2005

    • Author(s)
      I.Hasegawa, K.Yamauchi
    • Journal Title

      Differential Geometry-Dynamical Systems (掲載予定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Randers spaces of constant flag curvature induced by almost contact metric structures2004

    • Author(s)
      I.Hasegawa, V.S.Sabau, H.Shimada
    • Journal Title

      Hokkaido Mathematical Journal 33・1

      Pages: 215-232

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Geometric structures on tangent bundles2004

    • Author(s)
      I.Hasegawa, K.Yamauchi
    • Journal Title

      Proceedings of 39-th Symposium on Finsler Geometry

      Pages: 1-4

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Domination property of the set of upper bounds in ordered linear spaces2004

    • Author(s)
      N.Komuro
    • Journal Title

      Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis

      Pages: 217-226

    • Related Report
      2004 Annual Research Report

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Published: 2004-04-01   Modified: 2016-04-21  

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