| 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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| Budget Amount *help |
¥41,730,000 (Direct Cost: ¥32,100,000、Indirect Cost: ¥9,630,000)
Fiscal Year 2017: ¥8,580,000 (Direct Cost: ¥6,600,000、Indirect Cost: ¥1,980,000)
Fiscal Year 2016: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000)
Fiscal Year 2015: ¥8,580,000 (Direct Cost: ¥6,600,000、Indirect Cost: ¥1,980,000)
Fiscal Year 2014: ¥8,580,000 (Direct Cost: ¥6,600,000、Indirect Cost: ¥1,980,000)
Fiscal Year 2013: ¥7,670,000 (Direct Cost: ¥5,900,000、Indirect Cost: ¥1,770,000)
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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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