Self-similar groups and finite Gelfand pairs
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...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2007 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2007
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| Zitieren: | 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. |
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D’Angeli, D. Donno, A. 2019-06-20T03:07:43Z 2019-06-20T03:07:43Z 2007 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. 2000 Mathematics Subject Classification: 20E08, 20F65, 20F10, 05C25, 43A85, 43A90. 1726-3255 https://nasplib.isofts.kiev.ua/handle/123456789/157371 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 homogeneous with respect to the ultrametric distance. This gives rise to symmetric Gelfand pairs: we then compute the corresponding spherical functions. In the case of B and H(3) this result can also be obtained by using the strong property that the rigid stabilizers of the vertices of the first level of the tree act spherically transitively on the respective subtrees. On the other hand, this property does not hold in the case of I. We were introduced to beautiful theory of self-similar groups during our stay at the Mathematics Department of Texas A&M University. We thank Professors R. I. Grigorchuk, V. Nekrashevych and Z. Suni´c for ˇ useful discussions and warmest hospitality. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Self-similar groups and finite Gelfand pairs Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Self-similar groups and finite Gelfand pairs |
| spellingShingle |
Self-similar groups and finite Gelfand pairs D’Angeli, D. Donno, A. |
| title_short |
Self-similar groups and finite Gelfand pairs |
| title_full |
Self-similar groups and finite Gelfand pairs |
| title_fullStr |
Self-similar groups and finite Gelfand pairs |
| title_full_unstemmed |
Self-similar groups and finite Gelfand pairs |
| title_sort |
self-similar groups and finite gelfand pairs |
| author |
D’Angeli, D. Donno, A. |
| author_facet |
D’Angeli, D. Donno, A. |
| publishDate |
2007 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
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 homogeneous with
respect to the ultrametric distance. This gives rise to symmetric
Gelfand pairs: we then compute the corresponding spherical functions. In the case of B and H(3) this result can also be obtained by
using the strong property that the rigid stabilizers of the vertices
of the first level of the tree act spherically transitively on the respective subtrees. On the other hand, this property does not hold
in the case of I.
|
| isbn |
2000 Mathematics Subject Classification: 20E08, 20F65, 20F10, 05C25, 43A85, 43A90. |
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/157371 |
| citation_txt |
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. |
| work_keys_str_mv |
AT dangelid selfsimilargroupsandfinitegelfandpairs AT donnoa selfsimilargroupsandfinitegelfandpairs |
| first_indexed |
2025-12-07T18:56:53Z |
| last_indexed |
2025-12-07T18:56:53Z |
| _version_ |
1850876953128599552 |