2002 Fiscal Year Final Research Report Summary
A study of prehomogeneous vector spaces
| Project/Area Number |
13640027
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Yamaguchi University |
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Principal Investigator |
KASAI Shinichi Yamaguchi University, Faculty of Education, assistant professor, 教育学部, 助教授 (40224373)
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| Co-Investigator(Kenkyū-buntansha) |
KITAMOTO Takuya Yamaguchi University, Faculty of Education, assistant professor, 経済学部, 助教授 (30241780)
KASHIWAGI Yoshimi Yamaguchi University, Faculty of Economics, professor, 経済学部, 教授 (00152637)
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| Project Period (FY) |
2001 – 2002
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| Keywords | b-function / prehomogeneous |
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| Research Abstract |
The purpose of this study is to calculate the b-function of the special reducible prehomogeneous vector space, namely the regular simple prehomogeneous vector space related with SL(7) by the aid of microlocal method using the holonomy diagram of relative invariants.
From the result of Kimura, there are twelve regular simple prehomogeneous vector spaces which have two algebraically independent relative invariants. The b-functions of four of them are reduced to the case of irreducible prehomogeneous vector spaces. In this study, we have studied one of the remaining nontrivial eight cases. By the microlocal calculus on analysis of prehomogeneous vector spaces, we have determined the holonomy diagram and compute the b-function.
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