2013 Fiscal Year Final Research Report
Representation Theory of Symmetric Spaces over Finite or Local Fields
| Project/Area Number |
22540017
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
KATO Shin-ichi 京都大学, 理学(系)研究科(研究院), 教授 (90114438)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKANO Keiji 明石工業高等専門学校, 一般科目, 准教授 (40332043)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 対称空間 / 表現論 / 簡約群 / 有限体 / 局所体 |
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| Research Abstract |
We studied representations and harmonic analysis of symmetric spaces associated to reductive groups over finite or p-adic fields as a generalization of the representation theory of these groups. In the case of symmetric spaces over p-adic fields, we succeeded in constructing new examples of relatively cuspidal representations. We established criteria for tempered representations in the form analogous to the case of relatively cuspidal representations or square-integral representations. This is a natural extension of the criteria for group case. In the finite fields case, we studied a construction of relatively cuspidal representations on symmetric spaces by cohomological induction.
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