| Project/Area Number |
17K05209
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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) |
2017-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 局所関数等式 / 概均質ベクトル空間 / ゼータ超関数 / Clifford quartic form / polarization / F-多項式 / Catalecticant / homaloidal多項式 / 裏返し変換 / クラスター代数 / Legendre変換 / 極化 / 乗法的Legendre変換 / SubHankel行列 / 相対不変式 / hmaloidal多項式 / 係数付き団代数 / homaloidal polynomial / ゼータ関数 / Cluster代数 / homaloidal polynomials / Clifford quartic forms |
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| Outline of Final Research Achievements |
The following research results were obtained on pairs of polynomials satisfying local function equation.
(1) Explicit determination of local function equation associated with polarization of homaloidal polynomials and proof that prehomogeneity is maintained by polarization(2) Observation of polarization of polynomials satisfying local functional equation even if they are non-prehomogeneous homogeneous(3) Observation of prehomogenety of each uniform part of F-polynomials associated with cluster algebra with coefficients and observation of their relationship with projective manifolds(4) Observation of prehomogeneity of a section of Catalecticant determinant(5) Relationship between resultant and generalized resultants and prehomogeneous vector space
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| Academic Significance and Societal Importance of the Research Achievements |
局所関数等式の研究は整数論では保型形式、ゼータ関数などの整数論の研究で重要であり, 今までの流れでは局所関数等式を満たす多項式のタイプはそれらの分野では概均質タイプのみしか扱ってこなかったが, 非概均質タイプまで含めた今回の研究は今までにないタイプの局所関数等式やその背後にある空間の特性を調べたものなので,整数論で、新しい現象の発見につながることが期待できる.表現論の分野では, 概均質ベクトル空間は群がreductiveであるが, 今回の研究では群がSolvableなものも含んでいて局所関数等式が多変数になり, 等質錐に付随するLaplace-Fourier変換との関係など大いに期待される.
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