1998 Fiscal Year Final Research Report Summary
Studies on the theory of representations of groups and algebras
| Project/Area Number |
09304015
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (A)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
解析学
|
|---|
| Research Institution | KYOTO UNIVERSITY |
|---|
Principal Investigator |
HIRAI Takeshi Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70025310)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
YAMASHITA Hiroshi Hokkaido Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (30192793)
KIKUCHI Katsuhiko Kyoto Univ., Graduate School of Science, Assistant, 大学院・理学研究科, 助手 (50283586)
IKEDA Tamotsu Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (20211716)
NOMURA Takaaki Kyoto Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (30135511)
YOSHIDA Hiroyuki Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (40108973)
|
|---|
| Project Period (FY) |
1997 – 1998
|
| Keywords | representations of groups / representations of algebras / representations of semisimple Lie groups |
|---|
| Research Abstract |
1. Construction of irreducible unitary representations of infinite-dimensional groups, for instance, diffeomorphism groups of manifolds. Harmonic analysis on infinite-dimensional homogenoeous spaces, by means of infinite-dimensional version of Jordan triplets.
2. Application of the theory of representations to the number theory, and conversely study from the side of the theory of representations on the problems occurred in the number theory. Calculation of matrix elements of representations of explicit groups.
3. In the theory of quantum groups, we studied differential operators on them, especially invariant differential operators. Harmonic analysis on quantum groups, and studies on special functions on them appeared as matrix elements of representations.
4. Representation theory of finite dimensional semisimple Lie groups and its application to the theory of differential equations.
(1) Determination of intertwining operators, especially for discrete series.
(2) Irreducible decomposition of quasi-regular representations on generalized symmetric spaces.
(3) Embedding of discrete series into generalized principal series representations.
Here there appears essentially an intimate relation with differential equations.
5. Studies on the theory of representation of Lie superalgebras and of (generalized) Kac-Moody algebras. Calculation of commuting algebras and irreducible decompositions of tensor products of natural representations.
Kac-Moody algebras are in general infinite-dimensional and many algabraic results were obtained. However, here we studied anatic side of the theory. Further, we also studied applications to geometry.
|
