2003 Fiscal Year Final Research Report Summary
Lie theoretic construction of simply elliptic singularities and associated primitive forms
| Project/Area Number |
14540054
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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, Faculty of engineering, Professor, 工学部, 教授 (50210472)
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| Co-Investigator(Kenkyū-buntansha) |
SUZUKI Norio Kitami Institute of Technology, Faculty of engineering, associate Professor, 工学部, 助教授 (80211986)
WATANABE Fumihiko Kitami Institute of Technology, Faculty of engineering, associate Professor, 工学部, 助教授 (20274433)
IOHARA Kenji Kobe University, Faculty of Science, assistant, 理学部, 助手 (00322199)
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| Project Period (FY) |
2002 – 2003
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| Keywords | elliptic curve / double loop Lie algebra / unstable vector bundle / simply elliptic singularity / super Virasoro algebra / Verma module / Fock module / hypergeometric fuction |
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| Research Abstract |
There is well known correspondence of isomorphism classes of holomorphic vector bundles over elliptic curves and orbit spaces of double loop algebras with respect to adjoint actions of double loop groups. Using this correspondence and an action of double loop groups on the C^*-bundle on double loop Lie algebras, Yamada have characterized unstable holomorphic vector bundles over elliptic curves. From this results, we will construct simply elliptic singularities in terms of Lie algebras. But this results are obtained under a assumption of existence of double loop group invariant holomorphic functions on C^*-bundle over double loop Lie algebras. So we should prove the existence of them.
Watanabe has calculated the degeneration of connection formulas for Gauss hypergeometric functions.
Iohara and Koga have studied the structure of Verma modules of N=1 super Virasoro algebras. As applications, they construct Bernstein-Gel'fand-Gel'fand type resolutions. Moreover, they have analyzed the structure of the Fock modules over the N=1 super Virasoro algebras. As an application, they constructed the Bechi-Rouet-Stora-tyutin type resolutions.
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