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Horospherical model for holomorphic discrete series and horospherical Cauchy transform

Published online by Cambridge University Press:  14 July 2006

Simon Gindikin ,
Bernhard Krötz  and
Gestur Ólafsson
Simon Gindikin
Affiliation:
Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USAgindikin@math.rutgers.edu
Bernhard Krötz
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 Bonn, Germanykroetz@mpim.mpg-bonn.de
Gestur Ólafsson
Affiliation:
Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USAolafsson@math.lsu.edu
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Abstract

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We define a complex horospherical transform on an affine symmetric space $X=G/H$ of Hermitian type and show that it has no kernel on the representations of the $H$-spherical holomorphic discrete series.

Keywords

semisimple Lie groupssymmetric spaceshorosphereshorospherical transformCauchy kernelHardy spaces22E46
Type
Research Article
Information
Compositio Mathematica , Volume 142 , Issue 4 , July 2006 , pp. 983 - 1008
Copyright
Foundation Compositio Mathematica 2006