New developments of vertex algebra theory
Project/Area Number |
23654006
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Research Category |
Grant-in-Aid for Challenging Exploratory Research
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Allocation Type | Multi-year Fund |
Research Field |
Algebra
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Research Institution | Kyoto University |
Principal Investigator |
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Project Period (FY) |
2011 – 2013
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
|
Keywords | 頂点作用素代数 / D加群 / 変型量子化 / W代数 / アーク空間 / アフィンリー環 / 国際研究者交流 / 頂点代数 / 幾何学的表現論 / 国際情報交換 / 変形量子化 |
Research Abstract |
(1) We have introduced the notion of an asymptotic algebra of chiral differential operators. We then have constructed, via a chiral Hamiltonian reduction, one such algebra over a resolution of the intersection of the Slodowy slice with the nilpotent cone. We compute the space of global sections of this algebra thereby proving a localization theorem for affine W-algebras at the critical level. This is a joint work with T. Kuwabara and F. Malikov. (2) We introduced a notion of semi-infinite restriction functor, and shows that it is compatible with admissibility of representations of affine Kac-Moody algebras, enabling an inductive study of Kac-Wakimoto admissible representations.
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Report
(4 results)
Research Products
(68 results)
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[Presentation] W 代数の表現論2013
Author(s)
荒川知幸
Organizer
2013年度(第16回) 代数学賞受賞特別講演
Place of Presentation
京都大学
Year and Date
2013-03-22
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[Presentation] Rationality of W -algebras2012
Author(s)
Tomoyuki Arakawa
Organizer
The XXIX International Colloquium on Group-Theoretical Methods in Physics
Place of Presentation
Chern Institute of Mathematics Tianjin, China
Related Report
Invited
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