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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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. 73–92DOI 10.4171/RSMUP/121-5