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2007 Fiscal Year Final Research Report Summary

On the supercuspidal representations of reductive algebraic groups over local field

Research Project

Project/Area Number 16540035
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionOsaka Prefecture University

Principal Investigator

TAKAHASHI Tetsuya  Osaka Prefecture University, Faculty of Liberal Arts & Sciences, Professor (20212011)

Co-Investigator(Kenkyū-buntansha) KAWAZOE Mitsuru  Osaka Pref Univ., Faculty of Liberal Arts & Sciences, Associate Professor (10295735)
Project Period (FY) 2004 – 2007
Keywordsnon-Archimedean local field / supercuspidal representation / character formula / local Langlands correspondence / ε-factor
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.

  • Research Products

    (2 results)

All 2005

All Journal Article (2 results) (of which Peer Reviewed: 1 results)

  • [Journal Article] On some constants in the supercuspidal characters of GL_1, l a prime ≠ p2005

    • Author(s)
      Tetsuya Takahashi
    • Journal Title

      Transaction of the American Mathematical Society 357

      Pages: 2509-2526

    • Description
      「研究成果報告書概要(和文)」より
    • Peer Reviewed
  • [Journal Article] On some constants in the supercuspidal characters of GL_1,1a prime≠p2005

    • Author(s)
      Tetsuya, Takahashi
    • Journal Title

      Transaction of the AMS Society 357

      Pages: 2509-2526

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 2010-02-04  

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