| Budget Amount *help |
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥260,000 (Direct Cost: ¥200,000、Indirect Cost: ¥60,000)
Fiscal Year 2014: ¥260,000 (Direct Cost: ¥200,000、Indirect Cost: ¥60,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥260,000 (Direct Cost: ¥200,000、Indirect Cost: ¥60,000)
Fiscal Year 2011: ¥260,000 (Direct Cost: ¥200,000、Indirect Cost: ¥60,000)
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| Outline of Final Research Achievements |
The irreducible decomposition of scalar holomorphic discrete series representations when restricted to semisimple symmetric pairs (G,H) is explicitly known as the Kobayashi--Schmid rule. This was proved by Schmid for H compact and by Kobayashi for general H. More generally, Kobayashi's multiplicity-free theorem ('97) guarantees that the restriction π|H is multiplicity-free whenever (G,H) is a symmetric pair and π is an irreducible unitary highest weight module of scalar type. During the period of research, I studied the Penrose transform for indefinite Grassmannian manifolds, and as its application, obtained some branching laws of singular highest weight modules with respect to the pair (U(n,n), SO*(2n)). This gives an extension of the Kobayashi--Schmid formula to certain non-tempered unitary representations which are realized in Dolbeault cohomology groups over indefinite Grassmannian manifolds. The resulting branching rule is multiplicity-free and discretely decomposable.
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