Rendiconti del Seminario Matematico della Università di Padova


Full-Text PDF (166 KB) | Metadata | Table of Contents | RSMUP summary
Volume 121, 2009, pp. 73–92
DOI: 10.4171/RSMUP/121-5

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

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

(1) Section de Mathématiques, Université de Genève, Case Postale 64, 1211, Genève, Switzerland
(2) Section de Mathématiques, Université de Genève, Case Postale 64, 1211, 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.

No keywords available for this article.

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