2015 Fiscal Year Final Research Report
Studies on the standard Whittaker modules
| Project/Area Number |
24540027
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Aoyama Gakuin University |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 標準 Whittaker (g,K)-加群 / リー群の表現論 / 主系列表現 |
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| Outline of Final Research Achievements |
The main topic of this research is the analysis of the structure of the standard Whittaker (g,K)-modules of real reductive Lie groups. Obtained are the following results:
(1) In the cases of Spin(n,1), SL(3,R) and Sp(2,R), we determined the structure of the standard Whittaker (g,K)-modules. As byproducts of this research, we obtained a new method of constructing the central elements of the universal enveloping algebra of orthogonal Lie algebras, and we determined the composition series of the principal series representations of SL(3,R) and Sp(2,R).
(2) We proved that, if the group in question satisfies some conditions, the standard Whittaker (g,K)-modules of this group lie in a part of a coherent family.
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| Free Research Field |
リー群の表現論
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