Research of Representation Theory and Combinatorial Analysis and its applications to analytical and algebraical Number Theory

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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)).