2009 Fiscal Year Final Research Report
Representation Theory of Symmetric Spaces over Finite or Local Fields
| Project/Area Number |
18540026
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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 Kyoto University, 大学院・理学研究科, 教授 (90114438)
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| Co-Investigator(Kenkyū-buntansha) |
MATSUKI Toshihiko 京都大学, 大学院・理学研究科, 教授 (20157283)
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| Co-Investigator(Renkei-kenkyūsha) |
NISHIYAMA Kyo 青山学院大学, 理工学部, 教授 (70183085)
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) |
2006 – 2009
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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 |
As a natural generalization of the representation theory of reductive groups, we studied representations of symmetric spaces attached to these groups. In the case of groups over p-adic fields, we established criteria for (relatively) cuspidal representations and square-integral representations in the form analogous to the group case. Moreover we proved the symmetric space version of subrepresentation theorem. In the case of groups over finite fields, we studied a construction of cuspidal representations on symmetric spaces by cohomological induction.
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