104 research outputs found
The complex crown for homogeneous harmonic spaces
A theory of holomorphic extension of eigenfunctions on homogeneous harmonic
spaces is developed.Comment: 17 pages, 1 figure
Harmonic analysis for real spherical spaces
We give an introduction to basic harmonic analysis and representation theory
for homogeneous spaces attached to a real reductive Lie group . A
special emphasis is made to the case where is real spherical.Comment: Shortened title, typos fixed, more details on dual smooth Frobenius
reciprocity (now Lemma 6.6). 38 pages, lecture notes for the Sanya meeting on
spherical varieties. To appear in Acta Math. Sinic
Domains of holomorphy for irreducible unitary representations of simple Lie groups
We classify the domains of holomorphy of all Harish-Chandra modules of
irreducible unitary representations of simple non-compact Lie groups.Comment: revised version, to appear in Invent. math., 14 page
The tempered spectrum of a real spherical space
Let G/H be a unimodular real spherical space which is either absolutely
spherical or wave-front. It is shown that every tempered representation of G/H
embeds into a relative discrete series of a boundary degeneration of G/H. If in
addition G/H is of wave-front type it follows that the tempered representation
is parabolically induced from a discrete series representation of a lower
dimensional real spherical space. Final version. To appear in Acta Math.Comment: 64 page
The harmonic analysis of lattice counting on real spherical spaces
By the collective name of {\it lattice counting} we refer to a setup
introduced in Duke-Rudnick-Sarnak that aim to establish a relationship between
arithmetic and randomness in the context of affine symmetric spaces. In this
paper we extend the geometric setup from symmetric to real spherical spaces and
continue to develop the approach with harmonic analysis which was initiated in
Duke-Rudnick-Sarnak.Comment: Extended and revised version with 4 additional pages. To appear in
Documenta mat
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