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On Parabolic Subgroups and Hecke Algebras of Some Fractal Groups
Laurent Bartholdi, Rostislav I. Grigorchuk
We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, s…
On the Spectrum of Hecke Type Operators related to some Fractal Groups
Laurent Bartholdi, Rostislav I. Grigorchuk
We give the first example of a connected 4-regular graph whose Laplace operator's spectrum is a Cantor set, as well as several other computations of spectra following a common ``fi…
Lower Bounds on the Growth of Grigorchuk's Torsion Group
Laurent Bartholdi
In 1980 Rostislav Grigorchuk constructed a group of intermediate growth, and later obtained the following estimates on its growth : $e^{\sqrt{n}}\precsimγ(n)\precsim e^{n^β}…
Growth series of some hyperbolic graphs and Salem numbers
Laurent Bartholdi, Tullio G. Ceccherini-Silberstein
Extending the analogous result of Cannon and Wagreich for the fundamental groups of surfaces, we show that, for the l-regular graphs X associated to regular tessellations of hyperb…