Invariant trilinear forms on spherical principal series of real rank one semisimple lie groups

Salem Ben Said, Khalid Koufany, Genkai Zhang

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

Let G be a connected semisimple real-rank one Lie group with finite center. We consider intertwining operators on tensor products of spherical principal series representations of G. This allows us to construct an invariant trilinear form K ν indexed by a complex multiparameter ν = (ν1, ν2, ν3) and defined on the space of smooth functions on the product of three spheres in Fn, where F is either ℝ ℂ ℍ or O with n = 2. We then study the analytic continuation of the trilinear form with respect to (ν1, ν2, ν3), where we locate the hyperplanes containing the poles. Using a result due to Johnson and Wallach on the so-called «partial intertwining operator», we obtain an expression for the generalized Bernstein-Reznikov integral K ν (1⊗1⊗1) in terms of hypergeometric functions.

Original languageEnglish
Article number1450017
JournalInternational Journal of Mathematics
Volume25
Issue number3
DOIs
Publication statusPublished - 2014
Externally publishedYes

Keywords

  • Generalized Bernstein-Reznikov integrals
  • H-type groups
  • Intertwining operators
  • Invariant trilinear forms
  • Meromorphic continuation
  • Spherical principal series

ASJC Scopus subject areas

  • General Mathematics

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