1998 Fiscal Year Final Research Report Summary
Research of Representation Theory and Combinatorial Analysis and its applications to analytical and algebraical Number Theory
| Project/Area Number |
09640017
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Tokyo University of Mercantile Marine |
|---|
Principal Investigator |
IYANAGA Kenichi Tokyo Univ.of Mercantile Marine, Marine System Engineering ; Professor, 商船学部, 教授 (70114907)
|
|---|
| 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)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| 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 |
|---|
| 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)).
|
