## Abstract

Let F be a locally compact field of positive characteristic. In his thesis, the second author used the Langlands-Shahidi method to define γ-factors for the symmetric square and exterior square representations of the dual group of GL_{n}(F). We prove here that such γ-factors are characterized by local properties - including a multiplicativity property with respect to parabolic induction - and their role in global functional equations for L-functions. For this, we prove that a given cuspidal representation of GL _{n}(F) is the component at some place of a global automorphic representation, the ramification of which is controlled at other places. In fact, we use an equivalent result for l-adic Galois representations, due to O. Gabber and N. Katz, and transport it via the global Langlands correspondence proved by L. Lafforgue.

Original language | English |
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Pages (from-to) | 187-196 |

Number of pages | 10 |

Journal | American Journal of Mathematics |

Volume | 133 |

Issue number | 1 |

DOIs | |

State | Published - Feb 2011 |

Externally published | Yes |

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