| Budget Amount *help |
¥9,880,000 (Direct Cost: ¥7,600,000、Indirect Cost: ¥2,280,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2011: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
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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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