We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Let 
$E/F$ be a quadratic unramified extension of non-archimedean local fields and 
$\mathbb H$ a simply connected semisimple algebraic group defined and split over F. We establish general results (multiplicities, test vectors) on 
${\mathbb H} (F)$-distinguished Iwahori-spherical representations of 
${\mathbb H} (E)$. For discrete series Iwahori-spherical representations of 
${\mathbb H} (E)$, we prove a numerical criterion of 
${\mathbb H} (F)$-distinction. As an application, we classify the 
${\mathbb H} (F)$-distinguished discrete series representations of 
${\mathbb H} (E)$ corresponding to degree 
$1$ characters of the Iwahori-Hecke algebra.
