@article {
author = {Murnaghan, F.},
title = {Distinguished positive regular representations},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {43},
number = {Issue 4 (Special Issue)},
pages = {291-311},
year = {2017},
publisher = {Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {Let $G$ be a tamely ramified reductive $p$-adic group. We study distinction of a class of irreducible admissible representations of $G$ by the group of fixed points $H$ of an involution of $G$. The representations correspond to $G$-conjugacy classes of pairs $(T,\phi)$, where $T$ is a tamely ramified maximal torus of $G$ and $\phi$ is a quasicharacter of $T$ whose restriction to the maximal pro-$p$-subgroup satisfies a regularity condition. Under mild restrictions on the residual characteristic of $F$, we derive necessary conditions for $H$-distinction of a representation corresponding to $(T,\phi)$, expressed in terms of properties of $T$ and $\phi$ relative to the involution. We prove that if an $H$-distinguished representation arises from a pair $(T,\phi)$ such that $T$ is stable under the involution and compact modulo $(T\cap H)Z$ (here, $Z$ is the centre of $G$), then the representation is $H$-relatively supercuspidal.},
keywords = {Distinguished,representation,relatively supercuspidal},
url = {http://bims.iranjournals.ir/article_1165.html},
eprint = {http://bims.iranjournals.ir/article_1165_16668e3169e4cd8eb364090990daa092.pdf}
}