2002 Fiscal Year Final Research Report Summary
On the supercuspidal representations of reductive algebraic groups over local field
| Project/Area Number |
12640035
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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 | Osaka Prefecture University |
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Principal Investigator |
TAKAHASHI Tetsuya Osaka Pref. Univ., College of Integrated Arts & Sciences, Assocate Professor, 総合科学部, 助教授 (20212011)
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| Project Period (FY) |
2000 – 2002
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| Keywords | supercuspidal representation / character formula / ε-factor / local Langlands corjecture |
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| Research Abstract |
We get the following result in this term.
(1) Calculation of ε-factor for GL_1(F) × GL_1' (F)
We calculates the ε -factor of the representations of GL_1(F) × GL_{1'}(F) where 1 and 1' are distinct primes under some assumption. For the case GL_2(F) × GL_3(F), we need no assumption. It uses the local Langlands correspondence and non-Galois base change lift.
(2) Character formula for the supercuspidal representations of GL_1
We give a character formula for the irreducible supercuspidal representation of GL_1(F) for F a local field of the residual characteristic p ≠ 1.
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Research Products
(2 results)
