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.
Murnaghan, F. (2017). Distinguished positive regular representations. Bulletin of the Iranian Mathematical Society, 43(Issue 4 (Special Issue)), 291-311.
MLA
F. Murnaghan. "Distinguished positive regular representations". Bulletin of the Iranian Mathematical Society, 43, Issue 4 (Special Issue), 2017, 291-311.
HARVARD
Murnaghan, F. (2017). 'Distinguished positive regular representations', Bulletin of the Iranian Mathematical Society, 43(Issue 4 (Special Issue)), pp. 291-311.
VANCOUVER
Murnaghan, F. Distinguished positive regular representations. Bulletin of the Iranian Mathematical Society, 2017; 43(Issue 4 (Special Issue)): 291-311.
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