## Abstract

In this note we prove a certain multiplicity formula regarding the restriction of an irreducible admissible genuine representation of a 2-fold cover GL_{2}(F) of GL_{2}(F) to the 2-fold cover L_{2} (F) of SL_{2} (F), and find in particular that this multiplicity may not be one, a result that was recently observed for certain principal series representations in the work of Szpruch (2013). The proofs follow the standard path via Waldspurger’s analysis of theta correspondence between L_{2}(F) and PGL_{2}(F).

Original language | English |
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Pages (from-to) | 903-908 |

Number of pages | 6 |

Journal | Proceedings of the American Mathematical Society |

Volume | 144 |

Issue number | 2 |

DOIs | |

State | Published - 1 Feb 2016 |

Externally published | Yes |

## Keywords

- Covering groups
- Multiplicity formula
- Restriction of representations

## ASJC Scopus subject areas

- Mathematics (all)
- Applied Mathematics

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