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Study of Prehomogeneous vector spaces

Research Project

Project/Area Number 04640054
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionKYOTO UNIVERSITY

Principal Investigator

GYOJA Akihiko  Facutly of integrated Human studies, Kyoto University, Associate Professor, 総合人間学部, 助教授 (50116026)

Co-Investigator(Kenkyū-buntansha) NISHIYAMA Kyo  Facutly of integrated Human studies, Kyoto University, Associate Professor, 総合人間学部, 助教授 (70183085)
YOSHINO Yuji  Facutly of integrated Human studies, Kyoto University, Associate Professor, 総合人間学部, 助教授 (00135302)
MIYAMOTO Munemi  Facutly of integrated Human studies, Kyoto University, Professor, 総合人間学部, 教授 (00026775)
KATO Sin-ichi  Facutly of integrated Human studies, Kyoto University, Associate Professor, 総合人間学部, 助教授 (90114438)
西和田 公正  京都大学, 総合人間学部, 助教授 (60093291)
宇敷 重廣  京都大学, 大学院人間環境学研究科, 助教授 (10093197)
Project Period (FY) 1992 – 1993
Project Status Completed (Fiscal Year 1993)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1993: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1992: ¥1,300,000 (Direct Cost: ¥1,300,000)
Keywordsprehomogenous vector space / Lefschetz principle / Hecke algebra / R-matrix / automaton / Cohen-Macaulay module / Lie super algebra / irreducible unitary representation / 超幾何関数 / ジュリア集合 / CM正規環
Research Abstract

A.Gyoja improved the understanding of the Lefschetz principle in the theory of prehomogeneous vector spaces, using D-modules, mixed Hodge modules, perverse sheaves, etc. He also studied b-functions. Especially, he found an intimate relation between the b-functions of semi-invariants and the irreducibility of generalized Verma modules.
S.Kato showed that the duality of the representations of Hecke algebras can be obtained from an automorphism. He also constructed an R-matrix using Hecke algebras.
M.Miyamoto constructed stationary measures of automaton 90 and 150.
Y.Yoshino described the category of graded maximal Cohen-Macaulay modules, based on the Demazure representation of graded regular local rings. He also constructed a category of chain complexes which is equivalent to that of maximal Buchsbaum modules of finite projective dimension, and obtained a complete classification of such modules.
K.Nishiyama, with H.Furutsu, showed that all the irreducible unitary representation of the Lie superalgebra osp(m/n, R) can be realized using super dual pairs and the Weil representations.

Report

(3 results)
  • 1993 Annual Research Report   Final Research Report Summary
  • 1992 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] A.Gyoja(行者明彦): "Lefschetz principle in the theory of prehomogeneous vector spaces,Advnaced" Advanced Studies in Pure Mathematics. 21. 87-99 (1992)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] A.Gyoja(行者明彦): "Highest weight modules and b-functions of semi-invariants" Publications of the Research Institute for Mathematical Sciences. 30(発表予定). (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] S.Kato(加藤信一): "Duality for representations of a Hecke algebra" Proceedings of American Mathematical Society. 119. 941-946 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] M,Miyamoto(宮本宗実): "Staionary measures for automation reles 90 and 150" Journal of Mathematics of Kyoto University. 34(to appear). (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Y.Yoshino(吉野雄二): "Maximal Buchsbaum modules of finite projective dimension" Journal of Algebra. 159. 240-264 (1993)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] K.Nishiyama(西山享): "Super dual pairs and unitary highest weight modules of orthosymplectic algebras" Advances in Mathematics. 103(発表予定). (1994)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] A.Gyoja: "Lefschetz principle in the theory of prehomogeneous vector spaces" Admanced Studies in Pure Mathematics. vol.21. 87-99 (1992)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] A.Gyoja: "Highest weight modules and b-functions of semi-invariants" Publications of the Research Institute for Mathematical Sciences. vol.30. (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] S.Kato: "Duality for representations of a Heche algebra" Proceedings of American Mathematical Society. vol.119. 941-946 (1993)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] M.Miyamoto: "Staionary measures for automaton reles 90 and 150" Journal of Mathematics of kyoto Univ.vol.34, No.3 (to appear). (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] Y.Yoshino: "Maximal Buchsbaum modules of finite projective dimension" Journal of Algebra. vol.159. 240-264

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] K.Nishiyama: "Super dual pairs and unitary highest weight modules of orthosymplectic algebras" Advances in Mathematics. vol.103. (1994)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1993 Final Research Report Summary
  • [Publications] A.Gyoja(行者明彦): "Lefschetz principle in the theory of prehomogeneous vector spaces,Advances" Admanced Studies in Pure Mathematics. 21. 87-99 (1992)

    • Related Report
      1993 Annual Research Report
  • [Publications] A.Gyoja(行者明彦): "Highest weight modules and b-functions of Semi-invariants" Publications of the Research Institute for Mathematical Sciences. 30(発表予定). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] S.Kato(加藤信一): "Duality for representations of a Hecke algebra" Proceedings of American Mathematical Society. 119. 941-946 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] M.Miyamoto(宮本宗実): "Staionary measures for automaton reles 90 and 150" Journal of Mathematics of Kyoto University. 34(to appear). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] Y.Yoshino(吉野雄二): "Maximal Buchsbaum modules of finite projective dimension" Journal of Algebra. 159. 240-264 (1993)

    • Related Report
      1993 Annual Research Report
  • [Publications] K.Nishiyama(西山享): "Super dual pairs and unitary highest weight modules of orthosymplectic algebras" Advances in Mathematics. 103(発表予定). (1994)

    • Related Report
      1993 Annual Research Report
  • [Publications] 行者 明彦: "Lefschetz principle in the theory of prehomogeneous vector spaces" Advanced Studies in Pure Mathematics. 21. 87-99 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 行者 明彦: "On the regularity of prehomogeneous vector spaces" Proc.Japan.Academy. 68. 341-344 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 宇敷 重廣: "Bottcher′s Theorem and super-stalle manifolds for multi dimensional complex dynamical systems" Advanced Series in Dynamical Systems. 11. 168-184 (1992)

    • Related Report
      1992 Annual Research Report
  • [Publications] 加藤 信一: "Duality for representations of a Hecke algebra" Proceedings. of American. Math. soc.

    • Related Report
      1992 Annual Research Report
  • [Publications] 吉野 雄二: "Graded CM modules over graded normal CM domains." Journal of Math of Kyoto Univ.32. 73-92 (1992)

    • Related Report
      1992 Annual Research Report

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Published: 1992-04-01   Modified: 2016-04-21  

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