• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Representations of Lie groups

Research Project

Project/Area Number 10640218
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionMeijo University

Principal Investigator

OKAMOTO Kiyosato  Meijo University, Professor, 理工学部, 教授 (60028115)

Co-Investigator(Kenkyū-buntansha) SAITO Kimiaki  Meijo University, Professor, 理工学部, 教授 (90195983)
OZAWA Tetsuya  Meijo University, Professor, 理工学部, 教授 (20169288)
Project Period (FY) 1998 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2000: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1999: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1998: ¥1,100,000 (Direct Cost: ¥1,100,000)
Keywordsunitary representations / homogeneous space / functional analysis / global analysis / Poisson integral on the classical domain / Cauchy integral on the classical domain / Eigenfuctions of Laplacian / Invariant differential operators / リー群 / 表現論 / 多様体 / 微分幾何 / 関数解析 / 無限次元解析 / ホワイトノイズ
Research Abstract

Unitary representations of Lie groups are realized by the theory of Kirillov-Kostant using the symplectic structure on the adjoint orbits of Lie groups. The head investigator Okamoto worked with the investigator Ozawa about the symplectic structure.
The natural intertwining operator between the irreducible representation realized on the vector space of all smooth sections of homogeneous vector bundles on the boundary of classical domains and the representation realized on the vector space of all smooth sections of homogeneous vector bundles on the classical domains gives us the generalization of the Poisson integral. This generalized Poisson integral in cludes the Cauchy integral as a special case.
The most important fact here is that the invariant differential operator becomes the identity operator on the image of the intertwining operator. It follows that the generalized Poisson integral is an eigenfunction of invariant differential operators. In particular, if we consider the usual functions on the classical domains the results of Hua follows easily from this facts.
For the theory of automorphic functions on the classical domains, it is very important to generalize this to the case of vector bundle. One encounters, however, the crucial difficulty at once owing to the non commutativity of the operators.
In the course of computing the examples we found interesting formulas which contain the example given by Hua.
On the other hand, the head investigator Okamoto coorperated with investigator Saito about the integrability of integrals on the white noise which arises from the Feynman path integral for the infinite dimensional Lie groups.
The head investigator gave a talk at the symposium held at the research institute of Kyoto university.

Report

(4 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • 1998 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] K.Okamoto,M.Tsukamoto and K.Yokota: "Generalized Poisson and Cauchy kernel functions on classical domains"Japanese Journal of Mathematics. Vol.26 No.1. 51-103 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Okamoto,M.Tsukamoto and K.Yokota: "Vector bundle valued Poisson and Cauchy kernel functions on classical domains"Acta Applicandae Mathematicae. Vol.1. 1-10 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Ozawa and H.Sato: "Contact transformations and their Schwarzian derivatives"To appear in Nagoya Journal of Mathematics. (未定). (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] D.M.Chung and U.C.Ji and K.Saito: "Cauchy problems associated with the Levy Laplacian in white noise analysis"World Scientific Publishing Co.. Vol.2No.1. 131-153 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Saito and A.H.Tsoi: "Stochastic processes generated by functions of the Levy Laplacian Quantum information II"World Scientific Publishing Co.. Vo.1. 183-194 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Okamoto, M.Tsukamoto and K.Yokota: "Generalized Poisson and Cauchy kernel functions on classical domains"Japanese Journal of Mathematics. Vol.26 No.1. 51-103 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Okamoto, M.Tsukamoto and K.Yokota: "Vector bundle valued Poisson and Cauchy kernel functions on classical domains"Acta Applicandae Mathematicae. Vol.1. 1-10 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Ozawa and H.Sato: "Contact transformations and their Schwarzian derivatives"Nagoya Journal of Mathematics. (To appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] D.M.Chung and U.C.Ji and K.Saito: "Cauchy problems associated with the Levy Laplacian in white noise analysis"World Scientific Publishing Co.. Vol.2 No.1. 131-153 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Saito and A.H.Tsoi: "Stochastic processes generated by functions of the Levy Laplacian Quantum information II"World Scientific Publishing Co.. Vol.1. 183-194 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] K.Okamoto,M.Tsukamoto and K.Yokota: "Generalized Poisson and Cauchy kernel functions on classical domains"Japanese Journal of Mathematics. Vol.26 No.1. 51-103 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Okamoto,M.Tsukamoto and K.Yokota: "Vector bundle valued Poisson and Cauchy kernel functions on classical domains"Acta Applicandae Mathematicae. Vol.1. 1-10 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] T.Ozawa and H.Sato: "Contact transformations and their Schwarzian derivatives"To appear in Nagoya Journal of Mathematics. (未定). (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] D.M.Chung and U.C.Ji and K.Saito: "Cauchy problems associated with the Levy Laplacian in white noise analysis"World Scientific Publishing Co.. Vol.2 No.1. 131-153 (1999)

    • Related Report
      2000 Annual Research Report
  • [Publications] K.Saito and A.H.Tsoi: "Stochastic processes generated by functions of the Levy Laplacian Quantum information II"World Scientific Publishing Co.. Vo.1. 183-194 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] K. Okamoto, M. Tsukamoto and K. Yokota: "Generalized Poisson and Cauchy kernel functions on classical domains"Japanese Journal of Mathematics. Vol.26 No.1. (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] K. Okamoto, M. Tsukamoto and K. Yokota: "Vector bundle valued Poisson and Cauchy kernel functions on classical domains"Proceedings, World Scientific Publishing Co.. (未定). (2000)

    • Related Report
      1999 Annual Research Report
  • [Publications] K.Okamoto, M.Tsukamoto and K.Yokota: "Genaralked Poisson and Cancly kernel functions on classical domains" Nagoya Journal of Math.掲載決定. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Okamoto, M.Tsukamoto and K.Yokota: "Vector lurndle valvd Poisson and Candy keruel functlons on classical domains" Proceedings, World Sci.Pub.Co.掲載決定. (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Saito: "A Co group generated by the Levy Laplatian" Jour.of Stochastic Anal.and App.16. 567-584 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Saito: "A Co group generated by the Levy Laplatian II" Infinite dimensial Anal.and Q.1. 425-437 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] D.M.Chung, and K.Saito: "Candy problem associald, with the Levy Laplatian in white noise analysis" Infinite dimensial Anal.and Q.2 (掲載決定). (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Ozawa: "Finite order topological invariant of plane curves" Jour.of Knot Th and Its Romficatu. 8. 33-47 (1999)

    • Related Report
      1998 Annual Research Report

URL: 

Published: 1998-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi