Intertwining operators for the generalized principal series on a symmetric $R$-space

Jean-Louis Clerc (1)

1 IECL - Institut Élie Cartan de Lorraine

Three questions about the intertwining operators for the generalized principal series on a symmetric R-space are solved : description of the functional kernel, both in the noncompact and in the compact picture , domain of convergence, meromorphic continuation. A large use is made of the theory of positive Jordan triple systems. The meromorphic continuation of the intertwining integral is achieved via a Bernstein-Sato identity, and a precise description of the poles is obtained. 0 2000 Mathematics Subject Classification : 22E45, 43A80

Domaines: Mathématiques [math]

Jean-Louis Clerc. Intertwining operators for the generalized principal series on a symmetric $R$-space. Transactions of the American Mathematical Society, 2015, 367 (6), pp.4423-4458. ⟨10.1090/S0002-9947-2014-06327-7⟩. ⟨hal-01277889⟩