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Research on prehomogenecus vector spaces and representation theory of algebraic groups

Research Project

Project/Area Number 13440003
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionNagoya University

Principal Investigator

GYOJA Akihiko  Nagoya University, Graduate School of math., P, 大学院・多元数理科学研究科, 教授 (50116026)

Co-Investigator(Kenkyū-buntansha) FUJIWARA Kazuhiro  Nagoya University, Graduate School of math., P, 大学院・多元数理科学研究科, 教授 (00229064)
OKADA Soichi  Nagoya University, Graduate School of math., AP, 大学院・多元数理科学研究科, 助教授 (20224016)
UZAWA Toru  Nagoya University, Graduate School of math., P, 大学院・多元数理科学研究科, 教授 (40232813)
MUKAI Shigeru  Kyoto U., RIMS, P, 数理解析研究所, 教授 (80115641)
NOMURA Takaaki  Kyoto U., RIMS, AP, 大学院・理学研究科, 助教授 (30135511)
青本 和彦  名古屋大学, 大学院・多元数理科学研究科, 教授 (00011495)
Project Period (FY) 2001 – 2004
Project Status Completed (Fiscal Year 2004)
Budget Amount *help
¥8,400,000 (Direct Cost: ¥8,400,000)
Fiscal Year 2004: ¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2003: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2002: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2001: ¥2,200,000 (Direct Cost: ¥2,200,000)
Keywordsprehomogeneous vector sp. / algebraic group / representation / character sheaf / character sam / 指標層
Research Abstract

We have studied relations among the theory of prehomogeneous vector spaces, the theory of Lusztig's character sheaves, and the modular representation theory of Iwahori-Hecke algebras.
In particular, we found a curious relations between the theory of prehomogeneous vector spaces and the modular representation theory of Iwahori-Hecke algebras.
In the same time, we have made a considerable progress in the classification theory of prehomogeneous vector spaces. Since the summer of 1996,we have studied this classification, noticing a miraculous resemblance with the minimal model theory in the biratbnal geometry. We have made it dear that the central problems are the following.
Problem 1.Classify minirnal prehomogeneous vector spaces modulo flop.
Problem 2.Find the counter part of the flip.
I feel that we have already established conceptual foundation as for the first problem, but I believe that the actual classification needs more time.
I feel that we have recently made considerable progress, and that we have already obtained many examples of the (unknown) flip.
The above stated progress is not published, but I want to regard it as the main result of the present project of these years.

Report

(5 results)
  • 2004 Annual Research Report   Final Research Report Summary
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • 2001 Annual Research Report
  • Research Products

    (14 results)

All 2003 2002 2001 Other

All Journal Article (8 results) Book (1 results) Publications (5 results)

  • [Journal Article] Certain unipotent representations of finite Chevalley groups2002

    • Author(s)
      A.Gyoja
    • Journal Title

      Aun.Sci.de l'Ecole Norm.Sug. 35・3

      Pages: 437-444

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Vector bundles on a K3 surface2002

    • Author(s)
      S.Mukai
    • Journal Title

      Proc.ICM, Beijing

      Pages: 495-502

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Journal Article] Certain unipotent representations of finite Chevalley groups2002

    • Author(s)
      A.Gyoja
    • Journal Title

      Ann.Sci.de l'Erole Norm.Sup. 35-3

      Pages: 437-444

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Vector bundles on a K3 surface.2002

    • Author(s)
      S.Mukai
    • Journal Title

      Proc.ICM, Beijing

      Pages: 495-502

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Certain unipotent representations of finite Chevalley groups2002

    • Author(s)
      A.Gyoja
    • Journal Title

      Annales Scientifiques de l'Ecole Normale Sup. 35・3

      Pages: 437-444

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Symmetric varieties over arbitrary fields2001

    • Author(s)
      T.Uzawa
    • Journal Title

      C.R Acad.Sci.Paris 333・9

      Pages: 833-838

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Symmetric varieties over arbitrary fields2001

    • Author(s)
      T.Uzawa
    • Journal Title

      C.R Acad.Sci.Paris 333-9

      Pages: 833-838

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2004 Final Research Report Summary
  • [Journal Article] Symmetric varieties over arbitrary fields2001

    • Author(s)
      T.Uzawa
    • Journal Title

      C.R.Acad.Sci.Paris 333・9

      Pages: 833-838

    • Related Report
      2004 Annual Research Report
  • [Book] An introduction to invariants and moduli2003

    • Author(s)
      S.Mukai
    • Total Pages
      503
    • Publisher
      Cambridge University Press
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2004 Annual Research Report 2004 Final Research Report Summary
  • [Publications] T.Nomura: "Geometric norm equality related to the harmonicity of the Poisson kernel for homogeneous Siegel domains"J.Funct.Anal.. 198. 229-267 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] A.Gyoja, Y.Omoda: "Characteristic cycles of certain character sheaves"Indagations Mathematical. 12・3. 329-335 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.Gyoja: "Certain unipotent representations of finite Chevalley groups"Auncles scientifiques de l'Ecole Normale Superieure. 35・4. 437-444 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] A. Gyoja, Y. Omoda: "Characteristic cycles of certain character sheaves"Indagationes Mathematicae. (発表予定).

    • Related Report
      2001 Annual Research Report
  • [Publications] A. Gyoja: "Certain unipotent representations of finite Chevalley groups"Annales Scientifigues de L'Ecole Normale Superieure. (発表予定).

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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