## Abstract

Let S_{p2n}(F) be the metaplectic double cover of F where S_{p2n}(F) is a local field of characteristic 0. We use the Uniqueness of Whittaker model to define a metaplectic analog to Shahidi local coefficients and we use these coefficients to define gamma factors. We show that these gamma factors are multiplicative and satisfy the crude global functional equation. Then, we compute these factors in various cases and obtain explicit formulas for Plancherel measures. These computations are then used to prove some irreducibility theorems for parabolic induction on the metaplectic group over p-adic fields. In particular, we show that all principal series representations induced from unitary characters are irreducible. We also prove that parabolic induction from unitary supercuspidal representation of the Siegel parabolic sub group is irreducible if and only if a certain parabolic induction on SO_{2n+1}(F) is irreducible.

Original language | English |
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Pages (from-to) | 897-971 |

Number of pages | 75 |

Journal | Israel Journal of Mathematics |

Volume | 195 |

Issue number | 2 |

DOIs | |

State | Published - Jun 2013 |

Externally published | Yes |