1998 Fiscal Year Final Research Report Summary
On Metaplectic Forms of Classical Groups
| Project/Area Number |
09640050
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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 | University of the Ryukyus |
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Principal Investigator |
SUZUKI Toshiaki University of the Ryukyus Faculty of Science Department of Mathematical Science Professor, 理学部数理科学科, 教授 (50128485)
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| Co-Investigator(Kenkyū-buntansha) |
KOSUDA Masashi University of the Ryukyus Faculty of Scince Department of Mathemathical Science, 理学部数理科学科, 助手 (40291554)
SUGA Shu-ichi University of the Ryukyus Faculty of Science Department of Mathematical Scince A, 理学部数理科学科, 助教授 (30206388)
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| Project Period (FY) |
1997 – 1998
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| Keywords | Metaplectic group / Automorphic forms / Eisenstein series / Distinguished representations |
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| Research Abstract |
(1) We established a relation between Dirichlet series obtained as Fourier coefficients of metaplectic Eisenstein series and Rankin-Selberg convolutions of metaplectic forms.
(2) Unramified distinguished representations were determined and their Whittaker functins were explicitely given in some case. It was shown that the Rankin-Selberg convolutions of metaplectic forms against ditinguished metaplectic forms have Euler product. We propose a conjecture that auto-morphic distinguished representations on a n-fold metaplectic group of GL(nr) are parametrized by automorphic cuspidal representations of GL(r).
(3) We give a explicite formula for the dimension of Whittaker functionals on supercuspidal representations of metaplectic groups over a local field. Hence distinguished supercuspidal representations of metaplectic groups were determined.
(4) We proved the existence of a maximal compact subring of a local field with respect to 1-lilbert symbol. Hence it follows the existence of an open compact subgroup of a metaplectic group over a local field, which has very good properties.
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