The Action of Intertwining Operators on Spherical Vectors in the Minimal Principal Series of a Reductive Symmetric Space
نویسنده
چکیده
We study the action of standard intertwining operators on H-fixed generalized vectors in the minimal principal series of a reductive symmetric space G/H of Harish-Chandra's class. The main result is that-after an appropriate normalization-this action is unitary for the unitary principal series. This is an extension of previous work under more restrictive hypotheses on G and H. The present result implies the Maass-Selberg relations for Eisenstein integrals of the minimal principal series. These play a fundamental role in the most-continuous part of the Plancherel decomposition for G/H.
منابع مشابه
Composition Series and Intertwining Operators for the Spherical Principal Series
In this paper, we consider the connected split rank one Lie group of real type F4 which we denote by F4. We first exhibit F4 as a group of operators on the complexification of A. A. Albert's exceptional simple Jordan algebra. This enables us to explicitly realize the symmetric space F4/Spin(9) as the unit ball in R with boundary S . After decomposing the space of spherical harmonics under the a...
متن کاملAction of Intertwining Operators on Pseudo-spherical K-types
In this paper, we give a concrete description of the two-fold cover of a simply connected, split real reductive group and its maximal compact subgroup as Chevalley groups. We study the representations of the maximal compact subgroups called pseudospherical representations which appear with multiplicity one in the principal series representation. We introduce a family of canonically defined inte...
متن کاملOn the analytic properties of intertwining operators I: global normalizing factors
We provide a uniform estimate for the $L^1$-norm (over any interval of bounded length) of the logarithmic derivatives of global normalizing factors associated to intertwining operators for the following reductive groups over number fields: inner forms of $operatorname{GL}(n)$; quasi-split classical groups and their similitude groups; the exceptional group $G_2$. This estimate is a key in...
متن کاملIntertwining operators for the generalized principal series on a symmetric R-space
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 achieve...
متن کاملEuler factorization of global integrals
We consider integrals of cuspforms f on reductive groups G defined over numberfields k against restrictions ι∗E of Eisenstein series E on “larger” reductive groups G̃ over k via imbeddings ι : G → G̃. We give hypotheses sufficient to assure that such global integrals have Euler products. At good primes, the local factors are shown to be rational functions in the corresponding parameters q−s from ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996