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, cilt.28, sa.3, ss.609-618, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 28 Sayı: 3
  • Basım Tarihi: 2018
  • Dergi Adı: JOURNAL OF LIE THEORY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.609-618
  • Anahtar Kelimeler: Olshanski spherical pair, spherical function, spherical representation, automorphism group, homogeneous tree
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.