1998 Fiscal Year Final Research Report Summary
"Research on prehomogeneous vector spaces and micro-local analysis"
| Project/Area Number |
09640175
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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 |
解析学
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| Research Institution | Gifu University |
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Principal Investigator |
MURO Masakazu Gifu University, Faculty of Engineerings, Professor, 工学部, 教授 (70127934)
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| Co-Investigator(Kenkyū-buntansha) |
ASAKAWA Hidekazu Gifu University, Faculty of Engineerings, Research Assistant, 工学部, 助手 (00211003)
KOBAYASHI Takako Gifu University, Faculty of Engineerings, Associate Professor, 工学部, 助教授 (40252126)
MANDAI Takeshi Gifu University, Faculty of Engineerings, Associate Professor, 工学部, 助教授 (10181843)
AMANO Kazuo Gifu University, Faculty of Engineerings, Professor, 工学部, 教授 (40021761)
SHIGA Kiyoshi Gifu University, Faculty of Engineerings, Professor, 工学部, 教授 (10022683)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Representation / Prehomogeneous / Differential equation / Number theory / Zeta function / Vector space / Group |
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| Research Abstract |
(a) Singular invariant hyperfunctions on the space of n x n real symmetric matrices are discussed. We construct singular invariant hyperfunctions, i.e., invariant hyperfunctions whose supports are contained in the set S ={det(x) = O}, in terms of negative order coefficients of the Laurent expansions of the complex powers of the determinant function. In particular, we give an algorithm to determine the orders of poles of the complex powers of the determinant functions and the support of the singular hyperfunctions appearing in the principal part of the Laurent expansions of the complex powers.
(b) Singular invariant hyperfuncsions on the space of n x n complex and quaternion matrices are discussed. We give an algorithm to determine the orders of poles of the complex power of the determinant function and to determine exactly the support of singular invariant hyperfunctions, i.e., invariant hyperfunctions whose supports are contained in the set S : ={det(x) = O}, obtained as negative-order-coefficients of the Laurent expansions of the complex powers.
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