## Kyoto Journal of Mathematics

### On the distinguished spectrum of $\operatorname{Sp}_{2n}$ with respect to $\operatorname{Sp}_{n}\times\operatorname{Sp}_{n}$

#### Abstract

Given a reductive group $G$ and a reductive subgroup $H$, both defined over a number field $F$, we introduce the notion of the $H$-distinguished automorphic spectrum of $G$ and analyze it for the pairs $(\operatorname{GL}_{2n},\operatorname{Sp}_{n})$ and $(\operatorname{Sp}_{2n},\operatorname{Sp}_{n}\times\operatorname{Sp}_{n})$. In the first case we give a complete description by using results of Jacquet and Rallis as well as Offen and Yamana. In the second case we give an upper bound, generalizing vanishing results of Ash, Ginzburg, and Rallis, and a lower bound, extending results of Ginzburg, Rallis, and Soudry.

#### Article information

Source
Kyoto J. Math., Volume 58, Number 1 (2018), 101-171.

Dates
Accepted: 19 July 2016
First available in Project Euclid: 10 October 2017

https://projecteuclid.org/euclid.kjm/1507600817

Digital Object Identifier
doi:10.1215/21562261-2017-0019

Mathematical Reviews number (MathSciNet)
MR3776281

Zentralblatt MATH identifier
06873130

#### Citation

Lapid, Erez Moshe; Offen, Omer. On the distinguished spectrum of $\operatorname{Sp}_{2n}$ with respect to $\operatorname{Sp}_{n}\times\operatorname{Sp}_{n}$. Kyoto J. Math. 58 (2018), no. 1, 101--171. doi:10.1215/21562261-2017-0019. https://projecteuclid.org/euclid.kjm/1507600817

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