Harmonic Analysis for an Olshanski Pair Consisting of Stabilizers of the Horocycles of a Homogeneous Tree

S. C. Celik; S. Demir

doi:10.5802/jolt.1016

S. C. Celik; S. Demir

Journal of Lie Theory, Volume 28 (2018) no. 3, pp. 609-618

Abstract

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.

Zbl

DOI: 10.5802/jolt.1016

Classification: 20E08, 22A10, 43A65, 43A90
Keywords: Olshanski spherical pair, spherical function, spherical representation, automorphism group, homogeneous tree

@article{JOLT_2018_28_3_a0,
     author = {S. C. Celik and S. Demir},
     title = {Harmonic {Analysis} for an {Olshanski} {Pair} {Consisting} of {Stabilizers} of the {Horocycles} of a {Homogeneous} {Tree}},
     journal = {Journal of Lie Theory},
     pages = {609--618},
     year = {2018},
     volume = {28},
     number = {3},
     doi = {10.5802/jolt.1016},
     zbl = {1498.22004},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1016/}
}

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S. C. Celik; S. 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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