# Harmonic Analysis on Real Reductive Symmetric Spaces

@article{Delorme2002HarmonicAO, title={Harmonic Analysis on Real Reductive Symmetric Spaces}, author={P. Delorme}, journal={arXiv: Representation Theory}, year={2002} }

Let G be a reductive group in the Harish-Chandra class e.g. a connected seniisiniple Lie group with finite center, or the group of real points of a con nected reductive algebraic group defined over R. Let a be an involution of the Lie group G, H an open subgroup of the subgroup of fixed points of a. One decomposes the elements of L2(G/H) with the help of joint eigenfunctions under the algebra of left invariant differential operators under G on G/H. 2000 Mathematics subject classification… Expand

#### 15 Citations

The Plancherel Formula on Reductive Symmetric Spaces from the Point of View of the Schwartz Space

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Read Harmonic Analysis On Homogeneous Spaces Harmonic Analysis On Homogeneous Spaces

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This article is an expository paper. We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular… Expand

Harmonic Analysis on Homogeneous Spaces

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This article is an expository paper. We first survey developments over the past three decades in the theory of harmonic analysis on reductive symmetric spaces. Next we deal with the particular… Expand

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Author(s): Gomez, Raul | Abstract: /Let G be a simple Lie Group with finite center, and let K \subset G be a maximal compact subgroup. We say that G is a Lie group of tube type if G/K is a hermitian… Expand

Polynomial estimates for c-functions on reductive symmetric spaces

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The c-functions, related to a reductive symmetric space G/H and a fixed representation of a maximal compact subgroup K of G, are shown to satisfy polynomial bounds in imaginary directions.

Subrepresentation Theorem for p-adic Symmetric Spaces

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The notion of relative cuspidality for distinguished representations attached to p-adic symmetric spaces is introduced. A characterization of relative cuspidality in terms of Jacquet modules is given… Expand

Invariant trilinear forms for SL(3,R)

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Let F be a non-Archimedean local field. Let G be an algebraic group over F . A G-variety X defined over F is said to be multiplicity-free if for any admissible irreducible representation π of G (F )… Expand

An invariant measure for the loop space of a simply connected compact symmetric space

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Let X denote a simply connected compact Riemannian symmetric space, U the universal covering of the identity component of the group of automorphisms of X, and LU the loop group of U. In this paper we… Expand

The Plancherel theorem for a reductive symmetric space

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This chapter is based is on a series of lectures given at the meeting of the European
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