2004 Fiscal Year Final Research Report Summary
Research on prehomogenecus vector spaces and representation theory of algebraic groups
| 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)
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| Project Period (FY) |
2001 – 2004
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| Keywords | prehomogeneous vector sp. / algebraic group / representation / character sheaf / character sam |
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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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