-orbit closures on a -adic homogeneous space of infinite volume
J Jeoung, S Lim - arXiv preprint arXiv:2311.11118, 2023 - arxiv.org
J Jeoung, S Lim
arXiv preprint arXiv:2311.11118, 2023•arxiv.orgLet $\mathbb {K} $ be an unramified quadratic extension of $\mathbb {Q} _ {p} $ for a fixed $
p> 2$. Projective general linear groups $ G=\operatorname {PGL} _ {2}(\mathbb {K}) $ and $
H=\operatorname {PGL} _ {2}(\mathbb {Q} _ {p}) $ act transitively on Bruhat-Tits trees $ T_G
$ and $ T_H $, respectively. We identify $ G/H $ with the set of $ H $-subtrees $ G. T_ {H} $.
Let $\Gamma $ be a Schottky subgroup such that $\Gamma\backslash T_ {G} $ is infinite
volume and has an additional condition named high-branchedness, and let $\Lambda $ be …
p> 2$. Projective general linear groups $ G=\operatorname {PGL} _ {2}(\mathbb {K}) $ and $
H=\operatorname {PGL} _ {2}(\mathbb {Q} _ {p}) $ act transitively on Bruhat-Tits trees $ T_G
$ and $ T_H $, respectively. We identify $ G/H $ with the set of $ H $-subtrees $ G. T_ {H} $.
Let $\Gamma $ be a Schottky subgroup such that $\Gamma\backslash T_ {G} $ is infinite
volume and has an additional condition named high-branchedness, and let $\Lambda $ be …
Let be an unramified quadratic extension of for a fixed . Projective general linear groups and act transitively on Bruhat-Tits trees and , respectively. We identify with the set of -subtrees . Let be a Schottky subgroup such that is infinite volume and has an additional condition named high-branchedness, and let be its limit set. We classify -orbits in . Let . As a generalization of Ratner's theorem, if meets the convex core of , then the -orbit of is either dense or closed in .
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