Gelfand pairs associated with the action of graph automaton groups

نویسندگان
D’Angeli, Daniele ID 1
Cavaleri, Matteo ID 2
Donno, Alfredo ID 3

1 Dipartimento di Ingegneria, Università degli Studi Niccolò Cusano, Via Don Carlo Gnocchi, 3, 00166, Roma, Italy

2 Dipartimento di Ingegneria, Università degli Studi Niccolò Cusano, Via Don Carlo Gnocchi, 3, 00166, Roma, Italy

3 Università degli Studi Niccolò Cusano Dipartimento di Ingegneria Via Don Carlo Gnocchi, 3 00166 Roma, Italy

doi
10.22108/ijgt.2022.131733.1761
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