A Group of Automorphisms of the Rooted Dyadic Tree and Associated Gelfand Pairs
Daniele D'Angeli
Université de Genève, SwitzerlandAlfredo Donno
Université de Genève, Switzerland
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Abstract
In this paper we study the group of automorphisms of the rooted dyadic tree generated by translation by 1 and multiplication by an odd integer , showing that admits a self-similar presentation and it is isomorphic to the Baumslag–Solitar group . Moreover, we show that the action of on each level of the tree gives rise to a Gelfand pair.
Cite this article
Daniele D'Angeli, Alfredo Donno, A Group of Automorphisms of the Rooted Dyadic Tree and Associated Gelfand Pairs. Rend. Sem. Mat. Univ. Padova 121 (2009), pp. 73–92
DOI 10.4171/RSMUP/121-5