2005 Fiscal Year Final Research Report Summary
Constructive geometry of arithmetic quotients of symmetric spaces
| Project/Area Number |
14340004
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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 |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
ODA Takayuki The University of Tokyo, Graduate School of Math.-Sci., Professor, 大学院・数理科学研究科, 教授 (10109415)
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| Co-Investigator(Kenkyū-buntansha) |
TSUZUKI Masao Sophia University, Fac.of Sci.& Tech., Assist.Professor, 理工学部, 助手 (80296946)
KARIYAMA Kazutoshi Onomichi Univ., Fac.Ec.-Infom, Professor, 経済情報学部, 教授 (20123713)
HIRONAKA Yumiko Waseda Univ., Fac.Of Edu., Professor, 教育学部, 教授 (10153652)
IBUKIYAMA Tomoyshi Osaka Univ., Grad.of Sci., Professor, 大学院・理学研究科, 教授 (60011722)
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| Project Period (FY) |
2002 – 2005
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| Keywords | Automorphic forms / Spherical functions / Whittaker functions / Green currents / modular cycle / Automorphic forms / Spherical functions |
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| Research Abstract |
In the period of the project, we got the following results.
1.Explicit formula for Whittaker functions of SL(3,R) belonging to non-spherical principal series. (Published in 2004).
2.Given a pair of arithmetic quotients (X,Y), where X,Y are either type IV quotients, or quotients of the complex hyperball, and when Y is a divisor of X, we constructed the Green current of Y as an automorphic form. (Published in 2003).
3.We proved the confluence from Siegel-Whittaker functions to Whittaker functions for P_J principal series representations of Sp(2,R). (In press).
4.Together with Miki Hirano of Ehime University, we obtained the integral and power series expressions of the principal series Whittaker functions on GL(3,C) with minimal K-type. The project is still in progress.
5.The project to get explicit formula for P_J principal series representations of Sp(3,R) : The contents are finished. We are preparing a joint paper together with Miki Hirano and Taku Ishii of Chiba Inst. of Technology.
6.We maintained the monthly seminar on Automorphic Forms at Komaba.
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