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Journal of Lie Theory 28 (2018), No. 3, 609--618
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, Bebek-Istanbul 34342, Turkey

Selcuk Demir
Dept. of Mathematics, Dokuz Eylül University, Buca-Izmir 35160, Turkey

The 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.

Keywords: Olshanski spherical pair, spherical function, spherical representation, automorphism group, homogeneous tree.

MSC: 20E08, 22A10, 43A65, 43A90

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