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

Journal article, 2014

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. indexed by a complex multiparameter (v)under bar = (v1, v2, v3) and defined on the space of smooth functions on the product of three spheres in F-n, 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 (v1, v2, v3), 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-(v) under bar (1 circle times 1 circle times 1) in terms of hypergeometric functions.