2007 Fiscal Year Final Research Report Summary
On the supercuspidal representations of reductive algebraic groups over local field
| Project/Area Number |
16540035
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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 Prefecture University, Faculty of Liberal Arts & Sciences, Professor (20212011)
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| Co-Investigator(Kenkyū-buntansha) |
KAWAZOE Mitsuru Osaka Pref Univ., Faculty of Liberal Arts & Sciences, Associate Professor (10295735)
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| Project Period (FY) |
2004 – 2007
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| Keywords | non-Archimedean local field / supercuspidal representation / character formula / local Langlands correspondence / ε-factor |
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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 get the complete formula for the ε-factor of the representations of GL_1(F)×GL_{1'}(F) where 1 and 1' are distinct primes. For the proof of this formula, we use the local Langlands correspondence, non-Galois base change lift and Bushnell-Henniart's explicit correspondence.
(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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