On asymptotic dimension of groups.
Let be a maximal -order in a division quaternion algebra over which is split at the place . The present article gives an algorithm to compute a fundamental domain for the action of the group of units on the Bruhat-Tits tree associated to . This action is a function field analog of the action of a co-compact Fuchsian group on the upper half plane. The algorithm also yields an explicit presentation of the group in terms of generators and relations. Moreover we determine an upper bound...
* The authors thank the “Swiss National Science Foundation” for its support.We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are weakly maximal, and that the corresponding quasi-regular representations are irreducible. These (infinite-dimensional) representations are approximated by finite-dimensional quasi-regular representations. The Hecke algebras...