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SYMMETRIC PAIRS

Research Project

Project/Area Number 10440001
Research Category

Grant-in-Aid for Scientific Research (B).

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionRIKKYO UNIVERSITY

Principal Investigator

UZAWA Tooru  RIKKYO UNIV., COLLEGE OF SCIENCE, ASSIST.PROFESSOR, 理学部, 助教授 (40232813)

Co-Investigator(Kenkyū-buntansha) YAMADA Yuuji  RIKKYO UNIV., COLLEGE OF SCIENCE, ASSISTANT, 理学部, 助手 (40287917)
AOKI Noboru  RIKKYO UNIV., COLLEGE OF SCIENCE, ASSIST.PROFESSOR, 理学部, 助教授 (30183130)
FUJII Akio  RIKKYO UNIV., COLLEGE OF SCIENCE, PROFESSOR, 理学部, 教授 (50097226)
KUROKI Gen  TOHOKUUNIV., MATHEMATICAL INST., ASSISTANT, 大学院・理学研究科, 助手 (10234593)
HASEGAWA Kouji  TOHOKUUNN., MATHEMATICAL INST., LECTURER, 大学院・理学研究科, 講師 (30208483)
Project Period (FY) 1998 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥6,100,000 (Direct Cost: ¥6,100,000)
Fiscal Year 2000: ¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 1999: ¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 1998: ¥1,600,000 (Direct Cost: ¥1,600,000)
KeywordsSymmetric Pairs / Linear Algelvaic Groups / Involutions / Relative Trace Formake / Affineanalogues / 標数2の体 / 対称多様体 / 標数2の体上の代数群 / 佐武図式 / 制限ルート系 / 代数群 / シュバレー群 / 楕円曲線 / L-関数 / 超幾何関数 / 超局所化 / 構成可能層 / 対合 / 簡約代数群 / L関数の零点
Research Abstract

For the grant period, we have carried out research on diverse aspects of symmetric pairs. A symmetric pair, in its most primitive form, is a group G together with a automorphism σ of order two. Symmetric pairs appear quite naturally in mathematics. For example, one can associate a symmetric pair to symmetric spaces by letting G be the group of isometries and σ the involution with respect to a base point. Simple Lie groups, if the base field is not of characteristic two, appear as symmetric pairs for the general linear group, with finitely many exceptions. We give a brief summary of results obtained.
(a) Extension of basic theory to the characteristic two case. We have shown that the theory for Riemannian symmetric spaces carry over ; in particular, one has the notion of Satake diagrams.
(b) Construction of a model for symmetric varieties and their compactifications over the ring of integers.
(c) Arithmetical aspects. Connections with special values of the Epstein Zeta function and families of elliptic curves have been probed.
(d) Physical aspects. Connections with the face models have been probed.

Report

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

    (25 results)

All Other

All Publications (25 results)

  • [Publications] UZAWA,TOHRU: "Compactifications of symmetric vavieties and applications to representation theory"Representation Theory and Noncomutative Harmonic Analysis. 1082. 137-142 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] FUJII,AKIO: "A NOTE ON THE VALUES OF THE EPSTEIN ZETA FUNCTIONS AT THE CRITICAL POINTS"COMMENTARI math. Univ.Sancti Pauli. 49. 195-225 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] HASEGAWA,KOTI: "COMMUTING DIFFERENCE OPERATORS ARISING FROM THE ELLIPTIC C_2^1-FACE MODEL"J.MATH.PHYSICS. 40. 4549-4568 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] KUROKI,GEN: "BOSONIZATION AND INTEGRAL REPRESENTATION OF THE KNIZMNIK-ZAMOLODCHKOV-BERNARD ERNATION"Communications in Math.Physics. 204. 587-618 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yamada,Y: "Face Models with continnous parameters and its relation to Zn-symmetric vertex model of Belavin"Comment.Math.Univ.St.Paul.. 48. 49-76 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Aoki,N: "On the 2-Selmer groups of Elliptic curves arising from the congruent number problem"Comment.Math.Univ.St.Paul.. 48. 77-101 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 宇沢達(共著): "20世紀の予想(内のラングランズ哲学入門)"日本評論社. 235 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Uzawa, T: "Compactifications of symmetric varieties and applications to representation theory."Representation theory and non-commutative harmonic analysis. 1082. 137-142 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Fujii, A: "On the distribution of the zeros of the Riemann zeta function."Comment.Math.Univ.St.Paul. 49. 43-60 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Fujii, A.: "A Note on the values of the Epstein zeta functions at the critical points."Comment.Math.Univ.St.Paul.. 49. 195-225 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Yamada, Y.: "Face Models with Continuous Parameters and Its Relation to Zn-Symmetric Vertex Model of Belavin"Comment.Math.Univ.St.Paul.. 48. 49-76 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Aoki, N.: "On the 2-Selmer Groups of Elliptic Curves Arising from the Congruent Number Problem"Comment.Math.Univ.St.Paul.. 48. 77-101 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Hasegawa, K.: "Commuting difference operators arising from the elliptic C^<(1)>_2-face model"J.Math.Phys. vol 40 no.9. 4549-4568 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Kuroki, G.: "Bosonization and integral representation of solutions of the Knizhnik-Zamolodchikov-Bernard equations"Communication in Mathematical Physics. 204. 587-618 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] T.Uzawa: "On the tenson product of principal series representations of SL(2)"京都大学数理解析研究所講究録. 1-15 (2001)

    • Related Report
      2000 Annual Research Report
  • [Publications] A,Fujii,Ivic: "On the distributions of sums of zeros of the Riemann zeta function"Comm.Math.Univ.Sancti Pauli. 49・1. 23-42 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] A,Fujii: "A Note on the values of The Epstein zeta Functions at the critical points"Comm.Math.Univ.Sancti Pauli. 49・2. 195-225 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] N.Aoki: "Some remarks on the Hodge conjecture for Abelian varieties"Comm.Math.Univ.Sancti Pauli. 49・2. 177-194 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Aoki, Noboru: "On The 2-Selmon groups of Ellipticcurves arising from the * * problem"Commentar*i Ma Th. Uni. Sa*ch Pauli. 48. (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Uzawa, Tohru: "Elliptic curves, hypergem**ric functions and symmetric pai**"代数群と量子群の表現論、報告集. 2. 46-57 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Yamada, Yuji: "Facemodels with continuous parametes and its rel**** to *** - symmetric v*v*ex ur*** of B*lavin"Comm**tarii Ma **. Uni, Sancti Pauli. 48. (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Hasegawa, K. e*al: "Commuting difference ope*atons avising from the el*iptic C_2 - face model"Journal of Mathmatical physics. 40. 4549-4568 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] Kurdci, T*c*l*e: "Bosonization and integual rep*e*outa*u of solu A ** of *** Kni*unik-Za***clc***co* - * Equati*"C*mn. Math. Phys.. 204. 587-618 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] A.Fujii: "The clistribution of the zeroes of the Riemann zeta functions" Number Theory. 211-233 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] T.Uzawa: "Compactification of symmetric varieries and repnesentation theory" 表現論と非可換調和解析. (予定). 1-5

    • Related Report
      1998 Annual Research Report

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

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