2006 Fiscal Year Final Research Report Summary
Study on geometry and various invariants of symplectic space
| Project/Area Number |
17540095
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Chuo University |
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Principal Investigator |
TAKAKURA Tatsuru Chuo University, Faculty of Science and Engineering, Associate professor, 理工学部, 助教授 (30268974)
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| Co-Investigator(Kenkyū-buntansha) |
MIYOSHI Shigeaki Chuo University, Faculty of Science and Engineering, Professor, 理工学部, 教授 (60166212)
OCHIAI Hiroyuki Nagoya University, Graduate School of Mathematics, Associate Professor, 大学院多元数理科学研究科, 助教授 (90214163)
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| Project Period (FY) |
2005 – 2006
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| Keywords | symplectic quotient / coadjoint orbit / volume / irreducible representation / tensor product / asymptotic dimension / hypergeometric integral |
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| Research Abstract |
The head investigator Takakura (with T. Suzuki) published the result on an explicit formula for the volume of a symplectic quotient for a product of several coadjoint orbits of the special unitary group of degree three. The volume is regarded as a generating function of intersection pairings, and coincides with the asymptotic dimension of the invariant subspace of tensor product of irreducible representations. We also considered the similar problem for any compact Lie group, and derived a formula that expresses the asymptotic dimension as a finite sum. This is a vast generalization of those for the special unitary group of low degrees. However, in this generalization, we only treat the case when all the highest weights are regular. The other cases remain to be studied. In addition, since each term is given as a hypergeometric integral, the formula is not completely explicit. It is interesting to investigate these integrals. On the other hand, several years ago, we obtained another formula which expresses the asymptotic dimension as an infinite series. However, it turned out that the derivation has a subtle difficulty, concerned with the double limit process. So, we gave a rigorous proof of this infinite series formula, under the assumption that all highest weights are regular.
The investigator Miyoshi obtained a result on spinable foliations. The investigator Ochiai obtained results, on invariant distributions on pseude-Riemannian symmetric spaces, on spectral zeta function of non-commutative harmonic oscillators, on linear relations for multiple zeta values (with K. Ihara), on harmonic vector fields on hyperbolic 3-cone-manifold (with M. Fujii), on arithmetic structure of fake projective planes (with F. Kato), on multiple gamma functions and Mahler measures (with N. Kurokawa), on nilpotent orbits for symmetric pairs (with K. Nishiyama and C. B. Zhu), and successive approximations for a certain differential equation (with T. Hattori).
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Research Products
(15 results)
