| Project/Area Number |
09640017
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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 | Tokyo University of Mercantile Marine |
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Principal Investigator |
IYANAGA Kenichi Tokyo Univ.of Mercantile Marine, Marine System Engineering ; Professor, 商船学部, 教授 (70114907)
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| Co-Investigator(Kenkyū-buntansha) |
ARIKI Susumu Tokyo Univ.of Mercantile Marine, Marine System Engineering ; Associate Professor, 商船学部, 助教授 (40212641)
TANAKA Yohei Tokyo Univ.of Mercantile Marine, Marine System Engineering ; Associate Professor, 商船学部, 助教授 (00135295)
MATSUSHITA Osamu Tokyo Univ.of Mercantile Marine, Marine System Engineering ; Professor, 商船学部, 教授 (90092585)
NAKAMURA Shigeru Tokyo Univ.of Mercantile Marine, Marine System Engineering ; Professor, 商船学部, 教授 (00016940)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1998: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 1997: ¥1,700,000 (Direct Cost: ¥1,700,000)
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| Keywords | Representation Theory of Hecke algebras / Fibonacci numbers / number pi / quadratic equations over finite fields / 有限体上の2次方程式 / フィボナッチ数 / 多重完全数 / 2次形式論 |
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| Research Abstract |
Ariki contributed to solving the Dipper-James-Murphy Conjecture in the field of the Specht Theory related to the B-type Hecke algebras ; he also contributed to solving the Vigneras Conjecture related to the modular representation of general linear groups over local fields.
Tanaka obtained a formula describing the correspondence between two systems of basis of A-type Hecke algebras ; one parameterized by symmetric groups and another associated to certain pairs of the Young diagrams ; the formula is closely related to the Robinson-Schensted Correspondence.
Matsushita generalized Zeckendorf-Bunder Theorems on the Fibonacci numbers and showed that an arbitrary integer may be expressed as a sum of series {X_<alpha>} satisfying :
X_<alpha+2>=aX_<alpha>+X_1, X_1=1, X_2=a (n is an integer).
Nakamura simplified the proof of Stormer's Theorem on the relations between pi and values of arccotangent.
Tyanaga obtained a general formula to describe the numbers of solutions of the equation : x_1^2+・・・+x_*^2=a, (x_1 and a belong to F_p, x_i^2*x^2_j, p*1 (mod 4)).
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