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ON
$\text{Sp}$-DISTINGUISHED REPRESENTATIONS OF THE QUASI-SPLIT UNITARY GROUPS
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 20 / Issue 1 / January 2021
- Published online by Cambridge University Press:
- 17 April 2019, pp. 225-276
- Print publication:
- January 2021
-
- Article
- Export citation
-
We study
$\text{Sp}_{2n}(F)$-distinction for representations of the quasi-split unitary group 
$U_{2n}(E/F)$ in 
$2n$ variables with respect to a quadratic extension 
$E/F$ of 
$p$-adic fields. A conjecture of Dijols and Prasad predicts that no tempered representation is distinguished. We verify this for a large family of representations in terms of the Mœglin–Tadić classification of the discrete series. We further study distinction for some families of non-tempered representations. In particular, we exhibit 
$L$-packets with no distinguished members that transfer under base change to 
$\text{Sp}_{2n}(E)$-distinguished representations of 
$\text{GL}_{2n}(E)$.
