2010 Fiscal Year Final Research Report
Integrated study of probability and representation theory towards harmonic analysis on huge groups
| Project/Area Number |
19340032
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Nagoya University |
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Principal Investigator |
HORA Akihito Nagoya University, 大学院・多元数理科学研究科, 教授 (10212200)
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| Co-Investigator(Kenkyū-buntansha) |
OKADA Soichi 名古屋大学, 大学院・多元数理科学研究科, 教授 (20224016)
TATE Tatsuya 名古屋大学, 大学院・多元数理科学研究科, 准教授 (00317299)
HIRAI Takeshi 京都大学, 名誉教授 (70025310)
OBATA Nobuaki 東北大学, 大学院・情報科学研究科, 教授 (10169360)
SHIMOMURA Hiroaki 高知大学, 教育学部, 教授 (20092827)
KAWAZOE Takeshi 慶應義塾大学, 総合政策学部, 教授 (90152959)
YAMADA Hirofumi 岡山大学, 大学院・自然科学研究科, 教授 (40192794)
ARAI Hitoshi 東京大学, 大学院・数理科学研究科, 教授 (10175953)
NISHIYAMA Kyo 京都大学, 大学院・理学研究科, 准教授 (70183085)
ISHI Hideyuki 名古屋大学, 大学院・多元数理科学研究科, 准教授 (00326068)
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| 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)
INAHAMA Yuzuru 名古屋大学, 大学院・多元数理科学研究科, 准教授 (80431998)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 解析学 / 関数解析学 / 確率論 / 表現論 / 調和解析 |
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| Research Abstract |
Towards developing harmonic analysis on huge groups, we did integrated studies of probability theory and group representations. Harmonic analysis is a discipline which seeks deep mathematical structures by looking at symmetries of the objects and develops analysis relying on them. In this study, we are led to huge groups describing the symmetries because our objects are so big as to have an infinite degree of freedom. Main results among the ones we obtained are (i) classification and explicit formulas of the characters which are building blocks of harmonic analysis, and (ii) a series of theorems which construct a bridge between asymptotic behavior of representations of groups and probabilistic limit theorems.
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Research Products
(13 results)
