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)...
Gespeichert in:
| Veröffentlicht in: | Algebra and Discrete Mathematics |
|---|---|
| Datum: | 2007 |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут прикладної математики і механіки НАН України
2007
|
| Online Zugang: | https://nasplib.isofts.kiev.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| _version_ | 1862726259320029184 |
|---|---|
| author | D’Angeli, D. Donno, A. |
| author_facet | D’Angeli, D. Donno, A. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T18:56:53Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-157371 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| isbn | 2000 Mathematics Subject Classification: 20E08, 20F65, 20F10, 05C25, 43A85, 43A90. |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:56:53Z |
| publishDate | 2007 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Self-similar groups and finite Gelfand pairs D’Angeli, D. Donno, A. |
| title | 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_short | Self-similar groups and finite Gelfand pairs |
| title_sort | self-similar groups and finite gelfand pairs |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/157371 |
| work_keys_str_mv | AT dangelid selfsimilargroupsandfinitegelfandpairs AT donnoa selfsimilargroupsandfinitegelfandpairs |