Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2020; 57(6): 1491-1499

Online first article November 5, 2020      Printed November 30, 2020

https://doi.org/10.4134/BKMS.b200021

Copyright © The Korean Mathematical Society.

A fundamental domain for $PGL(2,\mathbb{F}_q[t])\backslash PGL\!\left(2,\mathbb{F}_q\!\left(\!(t^{-1})\!\right)\!\right)$

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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