2015 Fiscal Year Final Research Report
Geometry of instanton moduli spaces and representation theory
| Project/Area Number |
23340005
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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 | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
YOSHIOKA Kota 神戸大学, 理学研究科, 教授 (40274047)
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| Project Period (FY) |
2011-04-01 – 2016-03-31
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| Keywords | 代数学 / 幾何学 / 表現論 |
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| Outline of Final Research Achievements |
A duality between gauge theories and W-algebras was found by physicists Alday-Gaiotto-Tachikawa. We understand it as a mathematically rigorous statement that the equivariant cohomology group of a framed moduli space of instantons has a structure of a representation of a W-algebra, and various cohomology classes are described as vertex operators of the W-algebra. We study several results in this direction. In particular, jointly with Braverman-Finkelberg, we prove that the equivariant intersection cohomology group of a framed moduli space of instantons (more precisely its Uhlenbeck partial compactification) has an expected structure of a representation.
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| Free Research Field |
数学
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