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

Abstract

-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 BS q . Moreover, we show that the action of G on each level of the tree gives rise to a Gelfand pair.