A fundamental domain for PGL(2,Fq[t])＼PGL(2,Fq((t-1}))

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doi:10.4134/BKMS.b200021

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A fundamental domain for PGL(2,Fq[t])＼PGL(2,Fq((t-1}))

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Fundamental domain Bruhat-Tits tree

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초록

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 $\mathbb{P}^1(\mathbb{F}_q(\!(t^{-1})\!))$.

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 $\mathbb{P}^1(\mathbb{F}_q(\!(t^{-1})\!))$.

참고문헌 (4)

A. Broise-Alamichel, "Equidistribution and counting un-der equilibrium states in negative curvature and trees", pp.2019, Birkhauser
F. Bruhat, "Groupes reductifs sur un corps local", pp.5~251 (1972), Inst. Hautes Etudes Sci
F. Paulin, "On continued fraction expansions of quadratic irrationals in positive characteristic", Groups Geom. Dyn, 14(1), pp.81~105 (2020)[DOI]
J.-P. Serre, "Trees, Springer Monographs in Mathematics" (2003), Springer-Verlag

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Abstract

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