| 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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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥17,030,000 (Direct Cost: ¥13,100,000、Indirect Cost: ¥3,930,000)
Fiscal Year 2012: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2011: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2010: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2009: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2008: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
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| Keywords | W 代数 / アフィンリー環 / 頂点代数 / W代数 / 国際研究者交流 ドイツ、アメリカ、台湾 / 国際情報交換 / 国際研究者交流 / 頂点作用素代数 / カイラル微分作用素 / 臨界レベル / 随伴多様体 / 群の表現論 / 国際情報交流 / 指標公式 / カイラルD加群 |
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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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