11,850 research outputs found
Eisenstein integrals and induction of relations
I give a survey of joint work with Henrik Schlichtkrull on the induction of
certain relations among (partial) Eisenstein integrals for the minimal
principal series of a reductive symmetric space. I explain the application of
this principle of induction to the proofs of a Fourier inversion formula and a
Paley-Wiener theorem. Finally, the relation with the Plancherel decomposition
is discussed.Comment: Latex2e, 22 pp, Proc. Conf. `Analyse Harmonique Non Commutative
(colloque en l'honneur de Jacques Carmona)' CIRM, Luminy, 20-24 Mai, 200
A Paley-Wiener theorem for reductive symmetric spaces
Let X = G/H be a reductive symmetric space and K a maximal compact subgroup
of G. The image under the Fourier transform of the space of K-finite compactly
supported smooth functions on X is characterized.Comment: 31 pages, published versio
Paley-Wiener spaces for real reductive Lie groups
We show that Arthur's Paley-Wiener theorem for K-finite compactly supported
smooth functions on a real reductive Lie group G of the Harish-Chandra class
can be deduced from the Paley-Wiener theorem we established in the more general
setting of a reductive symmetric space.
In addition, we formulate an extension of Arthur's theorem to K-finite
compactly supported generalized functions (distributions) on G and show that
this result follows from the analogous result for reductive symmetric spaces as
well.Comment: Latex2e, 28 pages, change of definition of space P^* on p. 17 + minor
correction
Normalizations of Eisenstein integrals for reductive symmetric spaces
We construct minimal Eisenstein integrals for a reductive symmetric space G/H
as matrix coefficients of the minimal principal series of G. The Eisenstein
integrals thus obtained include those from the \sigma-minimal principal series.
In addition, we obtain related Eisenstein integrals, but with different
normalizations. Specialized to the case of the group, this wider class includes
Harish-Chandra's minimal Eisenstein integrals.Comment: 66 pages. Minor revisions. To be published in Journal of Functional
Analysi
-invariant cusp forms for reductive symmetric spaces of split rank one
Let be a reductive symmetric space of split rank and let be a
maximal compact subgroup of . In a previous article the first two authors
introduced a notion of cusp forms for . We show that the space of cusp
forms coincides with the closure of the -finite generalized matrix
coefficients of discrete series representations if and only if there exist no
-spherical discrete series representations. Moreover, we prove that every
-spherical discrete series representation occurs with multiplicity in
the Plancherel decomposition of .Comment: 12 page
Fully self-consistent calculations of nuclear Schiff moments
We calculate the Schiff moments of the nuclei 199Hg and 211Ra in completely
self-consistent odd-nucleus mean-field theory by modifying the
Hartree-Fock-Bogoliubov code HFODD. We allow for arbitrary shape deformation,
and include the effects of nucleon dipole moments alongside those of a
CP-violating pion-exchange nucleon-nucleon interaction. The results for 199Hg
differ significantly from those of previous calculations when the CP-violating
interaction is of isovector character.Comment: 7 pages, 2 figure
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