Self-similar groups and finite Gelfand pairs

• Date: 2018
• Main Authors: D’Angeli, Daniele, Donno, Alfredo
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: Rooted \(q\)-ary tree; ultrametric space; fractal group,labelling; rigid vertex stabilizer; 2-points homogeneous action,Gelfand pairs; spherical functions; 20E08; 20F65; 20F10; 05C25,43A85; 43A90
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/843
• Journal Title: Algebra and Discrete Mathematics

We study the Basilica group \(B\), the iterated monodromy group \(I\) of the complex polynomial \(z^2+i\) and the Hanoi Towers group \(H^{(3)}\). The first two groups act on the binary rooted tree, the third one on the ternary rooted tree. We prove that the action of \(B, I\) and \(H^{(3)}\) on each...