| Budget Amount *help |
¥42,640,000 (Direct Cost: ¥32,800,000、Indirect Cost: ¥9,840,000)
Fiscal Year 2022: ¥9,230,000 (Direct Cost: ¥7,100,000、Indirect Cost: ¥2,130,000)
Fiscal Year 2021: ¥8,450,000 (Direct Cost: ¥6,500,000、Indirect Cost: ¥1,950,000)
Fiscal Year 2020: ¥8,450,000 (Direct Cost: ¥6,500,000、Indirect Cost: ¥1,950,000)
Fiscal Year 2019: ¥8,450,000 (Direct Cost: ¥6,500,000、Indirect Cost: ¥1,950,000)
Fiscal Year 2018: ¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000)
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| Outline of Final Research Achievements |
1. In global analysis on a manifold X endowed with a group action, a novel approach, distinct from conventional differential equation methods, was formulated. This approach quantifies the topological condition of "proper actions" by estimating the "intersection volume." We advanced the foundational theory, particularly providing geometric criteria for determining when regular unitary representations on square-integrable spaces of X become tempered. Furthermore, we accomplished the classification for tempered reductive homogeneous spaces.
2. We provided a complete classification with explicit construction of "symmetry-breaking operators" between twisted exterior cotangent bundles for pairs consisting of a conformally flat manifold and its co-dimension one totally geodesic submanifold.
3. We developed the boundedness theorem and finiteness theorem of multiplicities for branching laws of infinite-dimensional representations by extending and refining our previous results.
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