Self-similar groups and finite Gelfand pairs

• Published in: Algebra and Discrete Mathematics
• Date: 2007
• Main Authors: D’Angeli, D., Donno, A.
• Format: Article
• Language: English
• Published: Інститут прикладної математики і механіки НАН України 2007
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/157371
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Self-similar groups and finite Gelfand pairs / D. D’Angeli, A. Donno // Algebra and Discrete Mathematics. — 2007. — Vol. 6, № 2. — С. 54–69. — Бібліогр.: 14 назв. — англ.

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 level is 2-points homog...