Çelik, Şermin ÇamGöral, H.2021-02-102021-02-1020200949-5932http://hdl.handle.net/10679/7288https://doi.org/10.1090/proc/14715The classification of the irreducible unitary representations of the stabilizer of the horocycles of a homogeneous tree of finite degree is well-known. 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.engrestrictedAccessarticle28360961800045610350000110.1090/proc/14715Olshanski spherical pairSpherical functionSpherical representationAutomorphism groupHomogeneous tree2-s2.0-85076817090