New developments of representation theory of W-algebras
| Project/Area Number |
25287004
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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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(Kenkyū-buntansha) |
山内 博 東京女子大学, 公私立大学の部局等, 准教授 (40452213)
山田 裕理 一橋大学, 経済学研究科(研究院), その他 (50134888)
和田 堅太郎 信州大学, 理学部, 准教授 (60583862)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥14,820,000 (Direct Cost: ¥11,400,000、Indirect Cost: ¥3,420,000)
Fiscal Year 2016: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2015: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2013: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
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| Keywords | 頂点作用素代数 / W代数 / アフィンリー環 / 随伴多様体 / ヒッグス枝 / シューア指数 / 群論（含群の表現論） / 代数学 / 群論 / 表現論 |
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| Outline of Final Research Achievements |
We have obtained a numerous results on W-algebras. In particular, the work with Anne Moreau on the W-algebras associated with the Define exceptional series has revealed un expected relationship between the Higgs branches of the four dimensional N=2 supernormal field theories and a certain geometric invariant of vertex algebras called the associated varieties. Based on the relationship, with Kazyuya Kawasetsu we showed the modularity of the Schur indices of our dimensional N=2 supernormal field theories in physics.
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Report
(5 results)
Research Products
(109 results)
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[Presentation] Associated varieties of vertex algebras2016
Author(s)
Tomoyuki Arakawa
Organizer
Exact operator algebras in superconformal field theories
Place of Presentation
Perimeter Institute for Theoretical Physics, Canada
Year and Date
2016-12-14
Related Report
Int'l Joint Research / Invited
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[Presentation] On Conway-Miyamoto correspondences2016
Author(s)
Hiroshi Yamauchi
Organizer
Workshop on Finite Groups, VOA, and Algebraic Combinatorics
Place of Presentation
Fogging University (Taiwan)
Year and Date
2016-03-23
Related Report
Int'l Joint Research / Invited
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[Presentation] Equivariant affine W-algebras2016
Author(s)
Tomoyuki Arakawa
Organizer
Nilpotent Orbits and Representation Theory
Place of Presentation
Centro di Ricerca Matematica Ennio De Giorgi (CRM), Pisa, Italy
Related Report
Int'l Joint Research / Invited
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[Presentation] On $\Z_k$-code vertex operator algebras2015
Author(s)
Hiromichi Yamada
Organizer
Taitung Workshop on group theory, VOA and algebraic combinatorics
Place of Presentation
National Taitung University, Zhiben Campus, Taitung, Taiwan
Year and Date
2015-03-07 – 2015-03-10
Related Report
Invited
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[Presentation] 冪零軌道とW代数2014
Author(s)
荒川 知幸
Organizer
第59回代数学シンポジウム
Place of Presentation
東京大学大学院数理科学研究科
Year and Date
2014-09-08 – 2014-09-11
Related Report
Invited
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[Presentation] Minimal models of W-algebras2014
Author(s)
Tomoyuki Arakawa
Organizer
Algebraic Lie theory and representation theory
Place of Presentation
The International Centre for Mathematical Sciences (ICMS), Edinburgh, UK.
Year and Date
2014-09-01 – 2014-09-05
Related Report
Invited
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