Rendiconti del Seminario Matematico della Università di Padova
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Published online: 2009-06-30
A Group of Automorphisms of the Rooted Dyadic Tree and Associated Gelfand PairsDaniele D'Angeli and Alfredo Donno (1) Université de Genève, Switzerland
(2) Université de Genève, Switzerland
In this paper we study the group G of automorphisms of therooted dyadic tree generated by translation by 1 andmultiplication by an odd integer q, showing that G admits aself-similar presentation and it is isomorphic to theBaumslag-Solitar group BSq. Moreover, we show that the actionof 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