Grant-in-Aid for Scientific Research (A)
|Research Institution||KYOTO UNIVERSITY|
HIRAI Takeshi Kyoto Univ., Graduate School of Science, Professor, 大学院・理学研究科, 教授 (70025310)
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)
梅田 亨 京都大学, 大学院・理学研究科, 助教授 (00176728)
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)
YAMASHITA Hiroshi Hokkaido Univ., Graduate School of Science, Associate Professor, 大学院・理学研究科, 助教授 (30192793)
|Project Fiscal Year
1997 – 1998
Completed(Fiscal Year 1998)
|Budget Amount *help
¥20,700,000 (Direct Cost : ¥20,700,000)
Fiscal Year 1998 : ¥9,100,000 (Direct Cost : ¥9,100,000)
Fiscal Year 1997 : ¥11,600,000 (Direct Cost : ¥11,600,000)
|Keywords||representations of groups / representations of algebras / representations of semisimple Lie groups / 群の表現 / 環の表現 / 半単純リー群の表現 / 表現論 / 無限次元群の表現論 / 無限次元環の表現 / 数論 / 確率過程 / 量子情報理論 / 無限次元均質空間上 / 調和解析|
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.