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The homothety classes of lattices in a two dimensional vector space over a nonarchimedean local field form a regular tree ${\mathcal{T}}$ of degree q + 1 on which the projective linear group acts naturally where q is the order of the residue field. We show that for any finite regular combinatorial graph of even degree q + 1, there exists a torsion free discrete subgroup ${\Gamma}$ of the projective linear group such that ${\mathcal{T}}/{\Gamma}$ is isomorphic to the graph.
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참고문헌 (5)
참고문헌 신청
Y. Benoist / 2003 / Five lectures on lattices in semisimple Lie groups, Géométries ά coubure négative ou nulle, groupes discrets et rigidité / Sémin. Congr. Soc. Math. France, Paris 18:117~176
Y. Ihara / 1966 / On discrete subgroups of the two by two projective linear groups over p-adic fields / J. Math. Soc. Japan 18:219~235
D. Jungnickel / 2013 / Graphs, networks and algorithms / Springer
J. -P. Serre / 2003 / Trees / Springer-Verlag
G. Shimura / 1970 / Introduction to the arithmetic theory of automorphic functions / Princeton University Press
Y. Ihara / 1966 / On discrete subgroups of the two by two projective linear groups over p-adic fields / J. Math. Soc. Japan 18:219~235
D. Jungnickel / 2013 / Graphs, networks and algorithms / Springer
J. -P. Serre / 2003 / Trees / Springer-Verlag
G. Shimura / 1970 / Introduction to the arithmetic theory of automorphic functions / Princeton University Press
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