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Automorphic Forms and Number Theory

Research Project

Project/Area Number 01540042
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

YAMAUCHI Masatoshi  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (30022651)

Co-Investigator(Kenkyū-buntansha) NISHIYAMA Kyo  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (70183085)
MATUKI Toshiko  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (20157283)
GYOUJYA Akihiko  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (50116026)
FUJIKI Akira  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (80027383)
SAITOU Hiroshi  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (20025464)
秋葉 知温  京都大学, 教養部, 教授 (60027670)
上田 哲生  京都大学, 教養部, 助教授 (10127053)
Project Period (FY) 1989 – 1990
Project Status Completed (Fiscal Year 1990)
Budget Amount *help
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1990: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1989: ¥1,400,000 (Direct Cost: ¥1,400,000)
KeywordsPrehomogenous Space / L-function / Gauss sum / Representation of quaternions / Hecke operator / Kahler manifold / Representation of Lie groups / flagmanifold / モジュライ空間 / ホッジ多様体 / 岩堀、ヘッケ代数 / ハッセの原理 / σ-共役類 / ノルム写像 / コンパクトケ-ラ-多様体 / moduli空間 / Weil Petersson計量 / 解析的変換 / 離散系列表現
Research Abstract

This research is mainly concerned with the field of modular forms and related topics. We believe we could obtain many fruitful results. The main results are as follows :
(1) H. Saito proves the functional equations of L functions with respect to the prehomogeneous space of the binary quadratic forms and gives their residues. Furthormore H. Saito defines the gaussian sum with respect to the matrix attached to the quadratic character of the quadratic forms over the finite field and showing this sum is a natural generalization of the classical gaussian sum, he gives some important applications to the prehomogeneous space of symmetric matrices and Siegel modular forms.
(2) H. Saito and M. Yamauchi consider the irreducible representation of the multiplicative group of the quaternion algebra over the local field and give an explicit form of the restrictions to Cartan subgroups and the character of these representations. Owing to this result, they give an application to the trace formula of Hec … More ke operators and give many important numerical examples of characteristic polynomials of Hecke operators for the modular groups of higher levels (cowork with H. Hijikata).
(3) A. Fujiki shows that the equivalence classes M of the representations from the fundamental group of the compact Kahler manifold to the complex reductive algebraic groups has the structure of the hyper Kahler space which admits a special C actions. Further in the associated Calabi family he showsthat the general fibre is isomorphic to M and special fibre is isomorphic to the moduli space of the Higgs bundle corresponding to the above representation.
(4) The open orbit of the prehomogenenous space acting the reductive algebraic group is an affine variety if and only if the space is regular. A. Gyoja gives a counter example to the conjecture that the regularity is a sufficient condition for the nonreductive case.
(5) T. Matuki describes the mapping which maps any representations of semisimple Lie groups to the principal series representations by the orbit structure over the flag manifolds. And for the classical simple Lie groups, he gives the symbolical expressions of the orbit structure of the flag manifolds. (cowork with T. Ohshima)
(6) K. Nishiyama defines the harmonic oscillator representation for the ortosymplectic Lie superalgebra and shows that it gives a unitary representation. This is an analogy of the Weil representations of the ordinary symplectic group. He also determines the wave front set of the Weil representations. Less

Report

(3 results)
  • 1990 Annual Research Report   Final Research Report Summary
  • 1989 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] 斎藤 裕: "A generation of Gauss sums and its applications to Siegel modularforms and αーfunctions" preprint.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 斎藤 裕: "Pepresentations of quaternuion algefras over local fields and trace formulas of Hecke operators" preprint.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 藤木 明: "Hyperhahlen struature on the moduli space of flat bundles" preprint.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 行者 明彦: "A counterexample in the theory of Prehomogeneous uector space" Proc.Japan Acod.66(1990). 66. 26-29 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 松本 敏彦: "Embeddingo of Piscrete Seiues into Principal series" Proceedings of a Corference Held in Copenhagen August to September. 147-175 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 西田 享: "Oscillator Representations for Orthosymplectic A lgefras" Journal of Algefra. 129. 231-261 (1990)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Hiroshi, Saito: "A generalization of Gauss sums and its application to Siegel modularforms and associated with the vector space of quadratic forms"

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Hiroshi, Saito: "Representations of quaternion algebras over local fields and trace formulas of Hecke operators"

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Akira, Fujiki: "Hyperkahler structure on the moduli space of flat bundles"

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Akihiko, Gyojya: "A counterexample in the theory of Prehomogeneous vector spaces" proc. Japan Acad.V. 66. 26-27 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Toshihiko, Matuki: "Embeddings of Discrete Series into Principal series" Proc. Conference Held Copenhagen. 147-175

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] Kyo, Nishiyama: "Oscillator Representations for Orthosymplectic Algebras" Journal of Algebra. V. 129. 231-262

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1990 Final Research Report Summary
  • [Publications] 斎藤 裕: "A generatization of Gauss Sums and its applications to Seegel modular forms and Lーfunctions associated with the vector space of quadraticforms"

    • Related Report
      1990 Annual Research Report
  • [Publications] 斎藤 裕: "Representations of quaternicon algebras over local fields and trace formulas of Heck orerators"

    • Related Report
      1990 Annual Research Report
  • [Publications] 藤木 明: "Hyperhaller structure on the moduli space of flat bundles"

    • Related Report
      1990 Annual Research Report
  • [Publications] 行者 明彦: "A counterexample in the cheory of prehomogeneous vector space" Proc.Japan Acad.66(1990). 66. 26-29 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 松木 敏彦: "Embeddings of Pescrete Series into Prin ciral reries" Proc.Conference Held in Copenhagen August to Septenber. 147-175 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 西山 享: "Oscillator Representalions for orthosymplctic Algebras" Journal of Algebra. 129. 231-261 (1990)

    • Related Report
      1990 Annual Research Report
  • [Publications] 藤木 明: "The moduli space of Kafler structures on areal compact symplectic manifold" Publ.RIMS kyoto Univ.24. 141-168 (1988)

    • Related Report
      1989 Annual Research Report
  • [Publications] 藤木 明: "Finite automorphism groups of Compact tori of dimension two" Publ.RIMS Kyoto. 24. 1-97 (1988)

    • Related Report
      1989 Annual Research Report
  • [Publications] 上田哲生: "Local structure of analytic transformations of two complex variables II" J.Math.Kyoto Univ.26. 232-261 (1988)

    • Related Report
      1989 Annual Research Report
  • [Publications] 上田哲生: "Psendoconcawe sets of general order and essential singevlarities of Analytic Set." Preprint pp 18.

    • Related Report
      1989 Annual Research Report
  • [Publications] 斎藤 裕: "On a Hasse principle for-conjagacy" J.Math.Kyoto Univ.24. 601-608 (1989)

    • Related Report
      1989 Annual Research Report
  • [Publications] 松木敏彦: "A description of discrete series for semisimple symmetric spaces II" Advanced Stud.Pure Math.14. 23-35 (1988)

    • Related Report
      1989 Annual Research Report

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Published: 1989-04-01   Modified: 2016-04-21  

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