Study on decomposition of unitary representations of groups and harmonic functions on branching graphs
| Project/Area Number |
23540197
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | Hokkaido University (2012-2013)
Nagoya University (2011) |
|---|
Principal Investigator |
HORA Akihito 北海道大学, 理学(系)研究科(研究院), 教授 (10212200)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
ISHI Hideyuki 名古屋大学, 大学院・多元数理科学研究科, 准教授 (00326068)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
MATSUMOTO Sho 名古屋大学, 大学院・多元数理科学研究科, 助教 (60547553)
OBATA Nobuaki 東北大学, 大学院・情報科学研究科, 教授 (10169360)
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Project Status |
Completed (Fiscal Year 2013)
|
| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
|---|
| Keywords | 関数解析 / 調和解析 / 確率論 / 表現論 |
|---|
| Research Abstract |
We intend to develop harmonic analysis on a large group, which plays a role in clarifying complex phenomena involving a huge number of factors. Our project aims at establishing a concrete framework by which one clearly understands decomposition of representations of a large group. For wreath products of a compact group, including the infinite symmetric group and infinite complex reflection groups, we took interactive approach from probability theory, group representations and potential theory, and obtained concrete and detailed results on such objects as group character formulas and their characterization, boundaries of the branching graph and minimal harmonic functions, and description of ergodic probabilities on the path space of the graph.
|
Report
(4 results)
Research Products
(15 results)
