| Project/Area Number |
13440003
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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 | Nagoya University |
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Principal Investigator |
GYOJA Akihiko Nagoya University, Graduate School of math., P, 大学院・多元数理科学研究科, 教授 (50116026)
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| Co-Investigator(Kenkyū-buntansha) |
FUJIWARA Kazuhiro Nagoya University, Graduate School of math., P, 大学院・多元数理科学研究科, 教授 (00229064)
OKADA Soichi Nagoya University, Graduate School of math., AP, 大学院・多元数理科学研究科, 助教授 (20224016)
UZAWA Toru Nagoya University, Graduate School of math., P, 大学院・多元数理科学研究科, 教授 (40232813)
MUKAI Shigeru Kyoto U., RIMS, P, 数理解析研究所, 教授 (80115641)
NOMURA Takaaki Kyoto U., RIMS, AP, 大学院・理学研究科, 助教授 (30135511)
青本 和彦 名古屋大学, 大学院・多元数理科学研究科, 教授 (00011495)
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| Project Period (FY) |
2001 – 2004
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| Project Status |
Completed (Fiscal Year 2004)
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| Budget Amount *help |
¥8,400,000 (Direct Cost: ¥8,400,000)
Fiscal Year 2004: ¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2003: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2002: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2001: ¥2,200,000 (Direct Cost: ¥2,200,000)
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| Keywords | prehomogeneous vector sp. / algebraic group / representation / character sheaf / character sam / 指標層 |
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| Research Abstract |
We have studied relations among the theory of prehomogeneous vector spaces, the theory of Lusztig's character sheaves, and the modular representation theory of Iwahori-Hecke algebras.
In particular, we found a curious relations between the theory of prehomogeneous vector spaces and the modular representation theory of Iwahori-Hecke algebras.
In the same time, we have made a considerable progress in the classification theory of prehomogeneous vector spaces. Since the summer of 1996,we have studied this classification, noticing a miraculous resemblance with the minimal model theory in the biratbnal geometry. We have made it dear that the central problems are the following.
Problem 1.Classify minirnal prehomogeneous vector spaces modulo flop.
Problem 2.Find the counter part of the flip.
I feel that we have already established conceptual foundation as for the first problem, but I believe that the actual classification needs more time.
I feel that we have recently made considerable progress, and that we have already obtained many examples of the (unknown) flip.
The above stated progress is not published, but I want to regard it as the main result of the present project of these years.
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