A fundamental domain for $PGL(2,\mathbb{F}_q[t])\backslash PGL\!\left(2,\mathbb{F}_q\!\left(\!(t^{-1})\!\right)\!\right)$
Bull. Korean Math. Soc. 2020 Vol. 57, No. 6, 1491-1499
https://doi.org/10.4134/BKMS.b200021
Published online November 5, 2020
Printed November 30, 2020
Sanghoon Kwon
Catholic Kwandong University
Abstract : We give a strong fundamental domain for the quotient of $PGL_2\!\left(\mathbb{F}_q(\!(t^{-1})\!)\!\right)$ by $PGL_2\!\left(\mathbb{F}_q[t]\right)$ as a subset of distinct ordered triple points of $\mathbb{P}^1(\mathbb{F}_q(\!(t^{-1})\!))$.
Keywords : Fundamental domain, Bruhat-Tits tree
MSC numbers : Primary 37P20; Secondary 20G25, 20H20
Supported by : This research was funded by the National Research Foundation of Korea (NRF) grant funded by the Korea government 2019R1I1A3A01058926
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