| Project/Area Number |
08454030
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
解析学
|
|---|
| Research Institution | Kobe University |
|---|
Principal Investigator |
NOUMI Masatoshi Kobe Univ., Dept.Math., Professor, 理学部, 教授 (80164672)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
SEKIGUCHI Hideko Kobe Univ., Dept.Math., Instructor, 理学部, 助手 (50281134)
TAKAYAMA Nobuki Kobe Univ., Dept.Math., Professor, 理学部, 教授 (30188099)
YAMAZAKI Tadashi Kobe Univ., Dept.Math., Professor, 理学部, 教授 (30011696)
SASAKI Takeshi Kobe Univ., Dept.Math., Professor, 理学部, 教授 (00022682)
TAKANO Kyoichi Kobe Univ., Dept.Math., Professor, 理学部, 教授 (10011678)
樋口 保成 神戸大学, 理学部, 教授 (60112075)
|
|---|
| Project Period (FY) |
1996
|
| Project Status |
Completed (Fiscal Year 1996)
|
| Budget Amount *help |
¥5,600,000 (Direct Cost: ¥5,600,000)
Fiscal Year 1996: ¥5,600,000 (Direct Cost: ¥5,600,000)
|
|---|
| Keywords | hypergeometric function / Macdonald polynomial / spherical function / Grassmannian / confluent hypergeometric function / configuration space / Macdonald多項式 / Grassmann多様体 |
|---|
| Research Abstract |
The main subject of the this research project has been to construct a new prototype of the theory of special functions, by originating a systematic study of hypergeometric special functions in many variables. In this repect, the following results have been obtained from the viewpoints of (1) quantum group symmetry of difference systems, (2) confluent hypergeometric functions and Hamiltonian systems, (3) geometry of configurations spaces, and (4) representation theory and integral transformations, respectively.
(1) M.Noumi developed a theory of sperical functions on quantum symmetric spaces in relation to quantum group symmetry. In terms of quantum groups, he gave a representation-theoretic realization of commuting families of q-difference operators and of the q-hypergeometric orthogonal polynomials of Macdonald type.
(2) K.Takano studied in detail the procedure of confluence for hypergeometric functions over the Grassmannians, namely the degeneration of a general regular singularity to a confluent singularity. He also clarified the structure of the spaces of initial values and the mechanism of degeneration in Hamiltonian systems of Painleve' type.
(3) T.Sasaki investigated the spaces of configurations of one nondegenerate quadratic hypersurface and n hyperplanes in the projective space. He determined the differential system for the associated hypergeometric integrals and described the symmetry of them. For the configurations in the projective plane, in particular, he consturcted explicit power series solutions and independent cycles, and clarified the relationship with Appell's hypergeometric functions.
(4) From the viewpoint of Penrose transformations in symmetric domains, H.Sekiguchi studied the generalization of hypergeometric integrals and hypergeometric differential equations to higher ranks. She also established the finite dimensionality of their solution spaces by means of the method of unitary representations.
|
