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

Abstract

We give a strong fundamental domain for the quotient of $PG{L}_2\left({\mathbb{F}}_q((t^{-1}))\right)$ by $PG{L}_2\left({\mathbb{F}}_q[t]\right)$ as a subset of distinct ordered triple points of ${\mathbb{P}}^1({\mathbb{F}}_q((t^{-1})))$.

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