JournalsrsmupVol. 121pp. 73–92

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

  • Daniele D'Angeli

    Université de Genève, Switzerland

  • Alfredo Donno

    Université de Genève, Switzerland
A Group of Automorphisms of the Rooted Dyadic Tree and Associated Gelfand Pairs cover
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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 BSq. Moreover, we show that the action of G 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