Transformation groups for geometric structures, global geometric analysis, and theory of branching laws of infinite dimensional representations
| Project/Area Number |
18340037
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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 |
Basic analysis
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| Research Institution | The University of Tokyo (2007-2009)
Kyoto University (2006) |
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Principal Investigator |
KOBAYASHI Toshiyuki The University of Tokyo, 大学院・数理科学研究科, 教授 (80201490)
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| Co-Investigator(Kenkyū-buntansha) |
OSHIMA Toshio 東京大学, 大学院・数理科学研究科, 教授 (50011721)
SEKIGUCHI Hideko 東京大学, 大学院・数理科学研究科, 准教授 (50281134)
寺田 至 東京大学, 大学院・数理科学研究科, 准教授 (70180081)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥16,500,000 (Direct Cost: ¥13,800,000、Indirect Cost: ¥2,700,000)
Fiscal Year 2009: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2008: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2007: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2006: ¥4,800,000 (Direct Cost: ¥4,800,000)
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| Keywords | ユニタリ表現 / リー群 / 極小表現 / 無重複表現 / 不連続群 / 分岐則 / 冪零軌道 / 可視的作用 / 多重積分 / シュレーディンガーモデル / フーリエ変換 / 高木レクチャー / 幕零軌道 / 幕零起動 |
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| Research Abstract |
Minimal representations are building blocks of unitary representations. During this period, we established the Schrodinger model of minimal representations of the indefinite orthogonal group, and determined a closed formula of the unitary inversion operator on the L^2-model on the isotropic cones, that generalizes the Euclidean Fourier transform. A new deformation theory was introduced in [1]. Further, I made systematic and synthetic applications of the original theory of visible actions on complex manifolds to multiplicity-free theorems, in particular, branching problems to symmetric pairs.
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Report
(6 results)
Research Products
(116 results)
