Study on symplectic space and its representation-theoretic structure
| Project/Area Number |
15540092
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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) |
2003 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥1,900,000 (Direct Cost: ¥1,900,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2003: ¥1,000,000 (Direct Cost: ¥1,000,000)
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| Keywords | Symplectic manifold / Moment map / Symplectic quotient / Coadjoint orbit / Character formula / Verlinde identity / Hypergeometric function / リーマン・ロッホの定理 |
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| Research Abstract |
The head investigator Takakura, in collaboration with Taro Suzuki, studied invariants of symplectic quotients for the products of coadjoint orbits of compact Lie groups, and obtained the following results.
First, for any simply-connected compact simple Lie group, we derived a general formula which expresses the above invariant as an infinite series. Secondly, for the 3 dimensional special unitary group, we obtained an another formula which expresses the invariant as a finite sum. Both of them are generalizations of earlier results by Takakura for the 2 dimensional special unitary group. Note that the first result may be regarded as an analogue of Witten's volume formula in 2 dimensional Yang-Mills theory. Our method is to reduce, via the fundamental theorem for symplectic quotients, the computation of characteristic numbers to a problem of representation theory of compact Lie groups or complex Lie algebras. More explicitly, we consider the trivial part of the tensor product of irreducib
… More
le representations and its asymptotic behavior. We can analyze them by the Weyl integration formula and the Verlinde identity for affine Lie algebras.
On the other hand, the investigator Miyoshi obtained a result on the smooth representability of the Euler classes of surface bundles.
The investigator Ochiai obtained results on non-commutative harmonic oscillator and the connection problem for the Heun differential equation, on polynomials associated with the hypergeometric functions with finite monodromy groups (with M.Yoshida), on absolute derivations and zeta functions (with N.Kurokawa and M.Wakabayashi), on explicit formulas for solutions of some vector-valued hypergeometric differential equations (with M.Fujii), on classification of completely integrable systems with large degree of freedom (with T.Oshima), on intersection theory for located cycles (with K.Mimachi and M.Yoshida), and on number-theoretic property for coefficients of certain polynomial solutions of the Painleve equations (with M.Kaneko). Less
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Report
(3 results)
Research Products
(25 results)
