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


Celik S. C., DEMİR S.

JOURNAL OF LIE THEORY, vol.28, no.3, pp.609-618, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 28 Issue: 3
  • Publication Date: 2018
  • Journal Name: JOURNAL OF LIE THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.609-618
  • Keywords: Olshanski spherical pair, spherical function, spherical representation, automorphism group, homogeneous tree
  • Dokuz Eylül University Affiliated: Yes

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.