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Gelfand pairs associated with the action of graph automaton groups | ||
| International Journal of Group Theory | ||
| مقاله 16، دوره 12، شماره 2، شهریور 2023، صفحه 55-66 اصل مقاله (643.65 K) | ||
| نوع مقاله: Ischia Group Theory 2020/2021 | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2022.131733.1761 | ||
| نویسندگان | ||
| Matteo Cavaleri1؛ Daniele D’Angeli1؛ Alfredo Donno* 2 | ||
| 1Dipartimento di Ingegneria, Università degli Studi Niccolò Cusano, Via Don Carlo Gnocchi, 3, 00166, Roma, Italy | ||
| 2Università degli Studi Niccolò Cusano Dipartimento di Ingegneria Via Don Carlo Gnocchi, 3 00166 Roma, Italy | ||
| چکیده | ||
| Graph automaton groups constitute a special class of automaton groups constructed from a graph. In this paper, we show that the action of any graph automaton group on each level of the rooted regular tree gives rise to a Gelfand pair. In particular, we determine the irreducible submodules of the action of such a group on the space of functions defined on each level of the tree, and we exhibit the corresponding spherical functions. | ||
| کلیدواژه‌ها | ||
| Graph automaton group؛ Gelfand pair؛ Rooted regular tree؛ $2$-points homogeneous action؛ Spherical function | ||
| مراجع | ||
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