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...
Gespeichert in:
| Datum: | 2007 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2007
|
| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/157371 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-157371 |
|---|---|
| record_format |
dspace |
| fulltext |
|
| spelling |
irk-123456789-1573712019-06-21T01:30:19Z Self-similar groups and finite Gelfand pairs D’Angeli, D. Donno, A. 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. 2007 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/157371 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
D’Angeli, D. Donno, A. |
| spellingShingle |
D’Angeli, D. Donno, A. Self-similar groups and finite Gelfand pairs Algebra and Discrete Mathematics |
| author_facet |
D’Angeli, D. Donno, A. |
| author_sort |
D’Angeli, D. |
| title |
Self-similar groups and finite Gelfand pairs |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2007 |
| url |
http://dspace.nbuv.gov.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. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT dangelid selfsimilargroupsandfinitegelfandpairs AT donnoa selfsimilargroupsandfinitegelfandpairs |
| first_indexed |
2025-07-14T09:48:42Z |
| last_indexed |
2025-07-14T09:48:42Z |
| _version_ |
1837615308479660032 |