2015 Fiscal Year Final Research Report
Properties of the associated spaces of polynomials which satisfy local functional equations
| Project/Area Number |
24540049
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Josai University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 局所関数等式 / homaloidal polynomial / Legendre変換 / Fourier変換 / Clifford algenbra / 概均質ベクトル空間 / Jordan algebra / 多項式の極化 |
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| Outline of Final Research Achievements |
It is known that one can associate local zeta functions satisfying a functional equation to the irreducible relative invariant of an irreducible regular prehomogeneous vector space. We construct polynomials of degree 4 (called Clifford quartic forms) that cannot be obtained from prehomogeneous vector spaces, but for which one can associate local zeta functions satisfying functional equations.The following study results were obtained. (1) We solved a conjecture by Etingof, Kazhdan and Polishchuk by using Clifford quartic forms(This is joint work with F.Sato).(2)We determined the multiplicative Legendre transformations for subHankel determinant and gave a conjecture for the form of the associated b-functions.This conjecture is still open.(This is joint work with H.Ishi) (3) We gave a conjecture for the form of b-fucntion and one of the gamma factor of local functional equation with respect to the polarization of a homaloidal polynomial (This conjecture was solved by F.Sato recently.)
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| Free Research Field |
整数論、表現論
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