## Abstract

Let SO_{2l} be the special orthogonal group, either split or quasi-split over a number field, and 1 < l < n. We compute the local integral, where data are unramified, derived from the global Rankin-Selberg construction for SO_{2l} × GL_{n}. In the general case, the local integral is difficult to compute directly, so instead it is transformed to an integral related to a construction for SO_{2n+1}×GL_{n}, which carries a Bessel model on SO_{2n+1}. For the quasisplit case, when l = n - 1 we are able to compute the local integral, by a modification of our recently introduced approach using invariant theory. This leads to another proof of our result for 1 < l < n, as well as a new proof of a known result regarding the unramified Bessel function.

Original language | English |
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Pages (from-to) | 137-184 |

Number of pages | 48 |

Journal | Israel Journal of Mathematics |

Volume | 191 |

Issue number | 1 |

DOIs | |

State | Published - Sep 2012 |

Externally published | Yes |

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