Journal of Lie Theory

no. 3
Harmonic Analysis for an Olshanski Pair Consisting of Stabilizers of the Horocycles of a Homogeneous Tree
Sermin Cam Celik1; Selcuk Demir2
1Dept. of Mathematics, Bogazici University, Bebek-Istanbul 34342, Turkey
2Dept. of Mathematics, Dokuz Eylül University, Buca-Izmir 35160, Turkey
Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 609-618
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.
DOI: 10.5802/jolt.1016
Classification: 20E08, 22A10, 43A65, 43A90
Keywords: Olshanski spherical pair, spherical function, spherical representation, automorphism group, homogeneous tree

Sermin Cam Celik  1 ; Selcuk Demir  2

1 Dept. of Mathematics, Bogazici University, Bebek-Istanbul 34342, Turkey
2 Dept. of Mathematics, Dokuz Eylül University, Buca-Izmir 35160, Turkey 
Sermin Cam Celik; Selcuk Demir. Harmonic Analysis for an Olshanski Pair Consisting of Stabilizers of the Horocycles of a Homogeneous Tree. Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 609-618. doi: 10.5802/jolt.1016
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     title = {Harmonic {Analysis} for an {Olshanski} {Pair} {Consisting} of {Stabilizers} of the {Horocycles} of a {Homogeneous} {Tree}},
     journal = {Journal of Lie Theory},
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     year = {2018},
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     doi = {10.5802/jolt.1016},
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