## Abstract

Let F be a p-adic field and let G(n)- and G0(n)- be the metaplectic double covers of the general symplectic group and symplectic group attached to a 2. n dimensional symplectic space over F. We show here that if n is odd then all the genuine irreducible representations of G(n)- are induced from a normal subgroup of finite index closely related to G0(n)-. Thus, we reduce, in this case, the theory of genuine admissible representations of G(n)- to the better understood corresponding theory of G0(n)-. For odd n we also prove the uniqueness of certain Whittaker functionals along with Rodier type of Heredity. Our results apply also to all parabolic subgroups of G(n)- if n is odd and to some of the parabolic subgroups of G(n)- if n is even. We prove some irreducibility criteria for parabolic induction on G(n)- for both even and odd n. As a corollary we show, among other results, that while for odd n, all genuine principal series representations of G(n)- induced from unitary representations are irreducible, there exist reducibility points on the unitary axis if n is even. We also list all the reducible genuine principal series representations of G(2)- provided that the F is not 2-adic.

Original language | English |
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Pages (from-to) | 160-193 |

Number of pages | 34 |

Journal | Journal of Algebra |

Volume | 388 |

DOIs | |

State | Published - 15 Aug 2013 |

Externally published | Yes |

## Keywords

- Metaplectic groups
- Representations of p-adic groups
- Whittaker functionals

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