Rendiconti del Seminario Matematico della Università di Padova


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Volume 121, 2009, pp. 73–92
DOI: 10.4171/RSMUP/121-5

Published online: 2009-06-30

A Group of Automorphisms of the Rooted Dyadic Tree and Associated Gelfand Pairs

Daniele D'Angeli[1] and Alfredo Donno[2]

(1) Université de Genève, Switzerland
(2) Université de Genève, Switzerland

In this paper we study the group G of automorphisms of the rooted dyadic tree generated by translation by 1 and multiplication by an odd integer q, showing that G admits a self-similar presentation and it is isomorphic to the Baumslag-Solitar group BSq. Moreover, we show that the action of G on each level of the tree gives rise to a Gelfand pair.

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D'Angeli Daniele, Donno Alfredo: A Group of Automorphisms of the Rooted Dyadic Tree and Associated Gelfand Pairs. Rend. Sem. Mat. Univ. Padova 121 (2009), 73-92. doi: 10.4171/RSMUP/121-5