
Journal of Lie Theory 28 (2018), No. 3, 609618 Copyright Heldermann Verlag 2018 Harmonic Analysis for an Olshanski Pair Consisting of Stabilizers of the Horocycles of a Homogeneous Tree Sermin Cam Celik Dept. of Mathematics, Bogazici University, BebekIstanbul 34342, Turkey sermincamcelik@gmail.com.tr Selcuk Demir Dept. of Mathematics, Dokuz Eylül University, BucaIzmir 35160, Turkey selcuk.demir@deu.edu.tr The classification of the irreducible unitary representations of the stabilizer of the horocycles of a homogeneous tree of finite degree is wellknown. In this article we use these stabilizers to form an Olshanski pair and then find all spherical functions of this pair. Finally we give realizations of the corresponding irreducible unitary representations. Keywords: Olshanski spherical pair, spherical function, spherical representation, automorphism group, homogeneous tree. MSC: 20E08, 22A10, 43A65, 43A90 [ Fulltextpdf (260 KB)] for subscribers only. 