2012 Fiscal Year Final Research Report
A comprehensive research of vertex algebras, especially the W-algebras
| Project/Area Number |
20340007
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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 (2010-2012)
Nara Women's University (2008-2009) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MATSUO Atsushi 東京大学, 数理科学研究科, 准教授 (20238968)
SUZUKI Takeshi 岡山大学, 自然科学研究科, 准教授 (30335294)
YAMAUCHI Hiroshi 東京女子大学, 現代教養部, 講師 (40452213)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMADA Hiromichi 一橋大学, 経済学研究科, 教授 (50134888)
MIYAMOTO Masahiko 筑波大学, 数理物質科学研究科, 教授 (30125356)
MATUZAWA Jyunichi 奈良女子大学, 理学部, 教授 (00212217)
KONNO Hitoshi 広島大学, 理学研究科, 准教授 (00291477)
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| Project Period (FY) |
2008 – 2012
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| Keywords | W 代数 / アフィンリー環 / 頂点代数 |
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| Research Abstract |
On admissible representations of affine Kac-Moody algebras, we proved the he conjecture of Frenkel, Kac and Wakimoto on the existence of two-sided BGG resolutions, the conjecture of Adamovic and Milas on the corresponding vertex operators algebra, and the conjecture of Feigin and Frenkel on their singular supports. On critical level representations of affine Kac-Moody algebras, we proved the new linkage principal and established a chiral Borel-Weil-Bott theorem. On W-algebras, we prove the C_2-cofinitness of the exceptional W-algebras discovered by Kac and Wakimoto and prove the admissible representations of affine Kac-Moody algebras. We obtained various results on the W-algebras at the critical levels.
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Research Products
(65 results)
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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
Year and Date
20120820-26
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