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

Clerc, Jean-Louis

doi:10.1090/S0002-9947-2014-06327-7

Intertwining operators for the generalized principal series on a symmetric $R$-space
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by Jean-Louis Clerc PDF

Trans. Amer. Math. Soc. 367 (2015), 4423-4458 Request permission

Abstract:

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, and 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.

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