Gelfand pairs associated with the action of graph automaton groups

Autor:	Matteo Cavaleri, Daniele D’Angeli, Alfredo Donno
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	graph automaton group gelfand pair rooted regular tree $2$-points homogeneous action spherical function Mathematics QA1-939
Zdroj:	International Journal of Group Theory, Vol 12, Iss 2, Pp 55-66 (2023)
Druh dokumentu:	article
ISSN:	2251-7650 2251-7669
DOI:	10.22108/ijgt.2022.131733.1761
Popis:	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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/c192fcbe9b43439e93497ae2bb0815a0 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF