2013 Fiscal Year Final Research Report
Analysis of minimal representations and branching laws of infinite-dimensional representations
| Project/Area Number |
22340026
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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 | The University of Tokyo |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
HIRACHI Kengo 東京大学, 大学院数理科学研究科, 教授 (60218790)
SEKIGUCHI Hideko 東京大学, 大学院数理科学研究科, 准教授 (50281134)
SASAKI Atsumu 東海大学, 理学部数学科, 講師 (60514453)
OSHIMA Toshio 城西大学, 理学部数学科, 教授 (50011721)
KOHNO Toshitake 東京大学, 大学院数理科学研究科, 教授 (80144111)
KANAI Masahiko 東京大学, 大学院数理科学研究科, 教授 (70183035)
OCHIAI Hiroyuki 九州大学, マス・フォア・インダストリ研究所・基礎理論研究部門 (90214163)
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| Project Period (FY) |
2010-04-01 – 2013-03-31
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| Keywords | 関数解析 / リー群 / 極小表現 / 表現論 / ユニタリ表現 / 簡約リー群 / 分岐則 / 可視的作用 |
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| Research Abstract |
Minimal representations are one of building blocks of unitary representations. Classic examples are the Weil representation, and intensive algebraic studies have been made since 1990s by many experts. In contrast, I proposed yet another geometric approach to minimal representations, by which we could expect a fruitful theory on global analysis by maximal symmetries. It includes a theory of unitary inversion operator on the L^2-model that generalizes the Euclidean Fourier transform with G. Mano ([Memoirs of AMS, 1000, (2011)]), a deformation theory of the Fourier transform in [Compositio Math. 2012], a theory of new "special functions" satisfying a certain ODE of order four with G. Mano, Hilgert, and Moellers in [Ramanujan J. 2011], and a generalization of the Schroodinger/Fock model in the framework of the Jordan algebra among others.
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