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## 談話会

タイトル Invariant trilinear forms on spherical principal series 2013年7月26日 16：45～18：00 Khalid Koufany　（University of Lorraine） 慶應義塾大学理工学部　14棟631A・B Let G be a connected semisimple real-rank one Lie group with nite center. We consider intertwining operators on tensor product of spherical principal series representations of G: This allows us to construct an invariant trilinear form K(f1 f2 f3); indexed by a complex multiparameter  = (1; 2; 3) and de ned on the space of smooth functions on the product of three spheres in Fn, where F is either R; C; H; or O: We then study the analytic continuation of the trilinear form with respect to (1; 2; 3), where we locate the hyperplanes containing the poles. We compute the residus at the poles of type one; their expression involves a covariant bidi erential operators. Finally, we obtain a closed formula for the generalized Bernstein-Reznikov integral K(1 1 1):