2010 Fiscal Year Final Research Report
Geometry of Moduli Spaces and its Application to Infinite Analysis
| Project/Area Number |
19340007
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo Metropolitan University (2010)
Yokkaichi University (2009)
Kyoto University (2007-2008) |
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Principal Investigator |
UENO Kenji 首都大学東京, 大学院・理工学研究科, 研究員 (40011655)
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| Co-Investigator(Kenkyū-buntansha) |
TOKUNAGA Hiroo 首都大学東京, 大学院・理工学研究科, 教授 (30211395)
KATO Tsuyoshi 京都大学, 大学院・理学研究科, 教授 (20273427)
KATO Fumiharu 京都大学, 大学院・理学研究科, 准教授 (50294880)
SHIMIZU Yuji 国際基督教大学, 教養学部, 教授 (80187468)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 代数科学 |
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| Research Abstract |
From conformal field theory with gauge symmetry constructed by Tsuchiya, Yamada and Ueno I and Joergen E. Andersen constructed modular functors so that we had topological filed theory for three manifolds. When the Lie algebra for gauge symmetry is sl(n, C) we proved that our topological field is isomorphic to the one constructed by Reshetikhin and Turaev by using GNS construction of representations of Hecke algebra. As a corollary to our proof we could also prove that conformal block bundles on the Teichmueller space of pointed Riemann surfaces of genus 0 carry unitary structure compatible with KZ connections.
Ueno also constructed a family of curves over a field of characteristic p, which contain multiple fiber pD where D is any divisor appearing a degeneration of a family of curves of genus 2 and p is any prime number.
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