Title of article :
GELFAND PAIRS ASSOCIATED WITH THE ACTION OF GRAPH AUTOMATON GROUPS
Author/Authors :
Cavaleri ، Matteo Dipartimento di Ingegneria - Università degli Studi Niccolò Cusano , D ANGELI ، Daniele Dipartimento di Ingegneria - Università degli Studi Niccolò Cusano , Donno ، Alfredo Dipartimento di Ingegneria - Universita degli Studi Niccolo Cusano
Abstract :
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.
Keywords :
Graph automaton group , Gelfand pair , Rooted regular tree , 2 , points homogeneous action , Spherical function
Journal title :
International Journal of Group Theory
Journal title :
International Journal of Group Theory
