2006 Fiscal Year Final Research Report Summary
Singularity Theory and Painleve Education-Lie Theoretical Construcion of Initial Space
| Project/Area Number |
16540049
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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 | Kitami Institute of Technology |
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Principal Investigator |
YAMADA Hiroshi Kitami Institute of Technology, 工学部, Technology Professor (50210472)
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| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Norio Kitami Institute of Technology, 工学部, associated Professor (80211986)
WATANABE Fumihiko Kitami Institute of Technology, 工学部, associate Professor (20274433)
IOHARA Kenji Kobe University, 理学部, assistant (00322199)
KAWAI Shingo Tokyo Institute of Technology, 理学研究科, assistant (60302931)
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| Project Period (FY) |
2004 – 2006
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| Keywords | elliptic curve / unstable holomorphic G-bundles / stable holomorphic G-bundles / simply elliptic singularity / anti-holomorphic connections / Lie group / affine Lie group / double loop algebra |
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| Research Abstract |
In this research, we showed the existence of non-trivial holomorphic functions on C^*-bundle on the double loop algebra E (g) which is invariant under a twisted gauge transformation of the double loop group E (G). Using these E (G)-invariant holomorphic functions, we gave a characterization of holomorphic unstable principal G-bundles over an elliptic curve. Furthermore, we classify the isomorphism classes of holomorphic semi-stable G-bundles over an elliptic curve.
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