2017 Fiscal Year Final Research Report
Infinite dimensional representations and global analysis
| Project/Area Number |
25247006
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
OSHIMA TOSHIO 城西大学, 理学部数学科, 教授 (50011721)
MATSUKI TOSHIHIKO 龍谷大学, 文学部, 教授 (20157283)
KOHNO TOSHITAKE 東京大学, 大学院数理科学研究科, 教授 (80144111)
OCHIAI HIROYUKI 九州大学, マス・フォア・インダストリ研究所, 教授 (90214163)
HIRACHI KENGO 東京大学, 大学院数理科学研究科, 教授 (60218790)
SEKIGUCHI HIDEKO 東京大学, 大学院数理科学研究科, 准教授 (50281134)
SASAKI ATSUMU 東海大学, 理学部数学科, 准教授 (60514453)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Keywords | 解析学 / 幾何学 / 表現論 / リー群 / 分岐則 / 不連続群 |
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| Outline of Final Research Achievements |
For manifolds with action of reductive group G, we proved a geometric criterion for the multiplicity of irreducible representations to be finite (also to be bounded) in the regular representation of X. In turn, we gave a criterion for reductive symmetric pair (G,H) such that branching laws of irreducible decomposition of G to H have finite multiplicities, and accomplished the classification theory. In this framework, we initiated a systematic study of symmetry breaking operators, and gave the first complete classification results in the setting motivated from conformal geometry.
We also constructed eigenfunctions on locally non-Riemannian symmetric spaces whoes eigenvalues are stable under local deformation of discontinuous groups.
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| Free Research Field |
解析学
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