Corpus ID: 15600041

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}
}
  • P. Delorme
  • Published 2002
  • Mathematics
  • arXiv: Representation Theory
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
The Plancherel Formula on Reductive Symmetric Spaces from the Point of View of the Schwartz Space
(a) to decompose the left regular representation of G in L2(G/H) into an Hilbert integral of irreducible unitary representations, (b) to decompose the Dirac measure at eH , where e is the neutralExpand
Read Harmonic Analysis On Homogeneous Spaces Harmonic Analysis On Homogeneous Spaces
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 particularExpand
Harmonic Analysis on Homogeneous Spaces
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 particularExpand
The Bessel-Plancherel theorem and applications
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 hermitianExpand
Polynomial estimates for c-functions on reductive symmetric spaces
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
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 givenExpand
Invariant trilinear forms for SL(3,R)
We give a detailed analysis of the orbit structure of the third power of the flag variety attached to SL(3,R). It turns out that 36 generalized Schubert cells split into 70 orbits plus one continuousExpand
D ec 2 01 9 P gl 2 is Multiplicity-Free as a PGL 2 × PGL 2-Variety
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
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 weExpand
The Plancherel theorem for a reductive symmetric space
This chapter is based is on a series of lectures given at the meeting of the European School of Group Theory in August 2000, Odense, Denmark. The purpose of the lectures was to explain theExpand
...
1
2
...

References

SHOWING 1-10 OF 50 REFERENCES
The principal series for a reductive symmetric space. II. Eisenstein integrals
In this paper we develop a theory of Eisenstein integrals related to the principal series for a reductive symmetric space G=H: Here G is a real reductive group of Harish-Chandra's class, ? anExpand
On the support of Plancherel measure
Abstract Let G be a real reductive group. As follows from Plancherel formula for G, proved by Harish-Chandra, only tempered representations of G contribute to the decomposition of the regularExpand
A class of parabolic K-subgroups associated with symmetric K-varieties
Let G be a connected reductive algebraic group defined over a field k of characteristic not 2, σ an involution of G defined over k, H a k-open subgroup of the fixed point group of σ, Gk (resp. Hk)Expand
Discrete series for semisimple symmetric spaces
We give a sufficient condition for the existence of minimal closed G-invariant subspaces of L2(G/H) for a semisimple symmetric space G/H. As a semisimple Lie group with finite center may always beExpand
Fonctions D(G/H)-Finies sur un Espace Symétrique Réductif
Abstract It is well known that, on R n, every smooth function annihilated by a finite codimensional ideal in the algebra of constant coefficient differential operators, is a linear combination ofExpand
Fourier analysis on semisimple symmetric spaces
A homogeneous space X = G/H of a connected Lie group G is called a symmetric homogeneous space if there exists an involution σ of G such that H lies between the fixed point group G and its identityExpand
Harmonic analysis on reductive symmetric spaces
We give a relatively non-technical survey of some recent advances in the Fourier theory for semisimple symmetric spaces. There are three major results: An inversion formula for the Fourier transform,Expand
Harmonic Analysis on Real Reductive Groups III. The Maass-Selberg Relations and the Plancherel Formula
Part I. The c-, jand p-functions 2. Some elementary results on integrals 120 3. A lemma of Arthur 125 4. Induced representations 127 5. Intertwining operators 129 6. The mapping T-+XT ..131 131 7.Expand
Fourier transforms on a semisimple symmetric space
Let G=H be a semisimple symmetric space, that is, G is a connected semisimple real Lie group with an involution ?, and H is an open subgroup of the group of xed points for ? in G. The main purpose ofExpand
Asymptotic Behavior of Spherical Functions on Semisimple Symmetric Spaces
Publisher Summary This chapter explains the asymptotic behavior of spherical functions on semisimple symmetric spaces. A K-finite simultaneous eigenfunction of the invariant differential operators onExpand
...
1
2
3
4
5
...