| Project/Area Number |
10440001
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| Research Category |
Grant-in-Aid for Scientific Research (B).
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | RIKKYO UNIVERSITY |
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Principal Investigator |
UZAWA Tooru RIKKYO UNIV., COLLEGE OF SCIENCE, ASSIST.PROFESSOR, 理学部, 助教授 (40232813)
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| 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)
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| Project Period (FY) |
1998 – 2000
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| Project Status |
Completed (Fiscal Year 2000)
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| 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)
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| Keywords | Symmetric 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 |
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| 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.
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